This class implements the multi-component mass transport equations proposed by Kerkhof-Geboers for fluid transport. More...

#include <compressible_multi_component_KG_equations_coupled.h>

Inheritance diagram for FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >:

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Collaboration diagram for FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >:

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Public Member Functions
Constructors, destructor, and initialization
	CompressibleMultiComponentKGEquationsCoupled (FuelCell::SystemManagement &system_management, boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData > data=boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >())
	Constructor. More...

virtual	~CompressibleMultiComponentKGEquationsCoupled ()
	Destructor. More...

virtual void	declare_parameters (ParameterHandler &param) const
	Declare parameters. More...

virtual void	initialize (ParameterHandler &param)
	Initialize parameters. More...

Local CG FEM based assemblers
virtual void	assemble_cell_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell matrix. More...

virtual void	assemble_cell_residual (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell residual. More...

virtual void	assemble_bdry_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary matrix. More...

virtual void	assemble_bdry_residual (FuelCell::ApplicationCore::FEVector &bdry_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary residual. More...

Accessors and info
const std::vector< double > &	get_inlet_outlet_velocity_max () const
	This function returns `inlet_outlet_velocity_max`. More...

const double	get_inlet_outlet_velocity_mixture_max () const
	This function returns `inlet_outlet_velocity_mixture_max`. More...

const bool	get_use_parabolic_profile () const
	This function tells the application if the user wishes to use a parabolic profile for a boundary condition. More...

const double	get_inlet_outlet_velocity_channel_base () const
	This function tells the application the height [cm] of the base of the channel with respect to origin. More...

const double	get_inlet_outlet_velocity_channel_roof () const
	This function tells the application the height [cm] of the roof of the channel with respect to origin. More...

const int	get_inlet_outlet_boundary_ID () const
	This function tells the application the boundary id to apply velocity profile equation to. More...

const std::string	get_press_vel_comp_apply_to () const
	Outputs which component to apply variable boundary equation to (i.e. More...

const std::string	get_inlet_outlet_velocity_mixture_equation () const
	If `get_use_parabolic_profile()` is false then user can specify an equation to use for velocity profile at boundary. More...

const std::map< unsigned int, std::string >	get_gas_species_map () const
	`get_gas_species_map()` returns a map relating the different KG species equations to the desired gas species being simulated; e.g 1:oxygen, 2:water vapour, 3:nitrogen means that the first 3 KG equations (Mass Cons., Mom. More...

const unsigned int	get_num_of_species () const
	If returns the number of species to use in the parameter file. More...

virtual void	print_equation_info () const
	This function prints out the equations info. More...

Public Member Functions inherited from FuelCellShop::Equation::EquationBase< dim >
const couplings_map &	get_internal_cell_couplings () const
	This function returns `internal_cell_couplings` of a derived equation class. More...

const couplings_map &	get_internal_flux_couplings () const
	This function returns `internal_flux_couplings` (DG FEM only) of a derived equation class. More...

const component_materialID_value_map &	get_component_materialID_value () const
	This function returns `component_materialID_value` of a derived equation class. More...

const component_boundaryID_value_map &	get_component_boundaryID_value () const
	This function returns `component_boundaryID_value` of a derived equation class. More...

const std::vector< BoundaryType > &	get_boundary_types () const
	This function returns `boundary_types` of a derived equation class. More...

const std::vector< std::vector < BoundaryType > > &	get_multi_boundary_types () const
	This function returns `multi_boundary_types` of a derived equation class. More...

const std::vector< OutputType > &	get_output_types () const
	This function returns `output_types` of a derived equation class. More...

const std::vector< std::vector < OutputType > > &	get_multi_output_types () const
	This function returns `multi_output_types` of a derived equation class. More...

const std::string &	get_equation_name () const
	This function returns `equation_name` of a derived equation class. More...

const std::vector< unsigned int > &	get_matrix_block_indices () const
	This function returns `matrix_block_indices` of a derived equation class. More...

const std::vector< unsigned int > &	get_residual_indices () const
	This function returns `residual_indices` of a derived equation class. More...

Protected Member Functions
Local CG FEM based assemblers - make_ functions
template<typename INFO >
void	make_assemblers_generic_constant_data (const INFO &InFo, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This function computes Computational constants and Local CG FEM based assemblers - constant data (generic). More...

virtual void	make_assemblers_cell_constant_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info)
	This function computes Local CG FEM based assemblers - constant data (cell) and allocates the memory for. More...

virtual void	make_assemblers_bdry_constant_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info)
	This function computes Local CG FEM based assemblers - constant data (boundary) and allocates the memory for. More...

virtual void	make_assemblers_cell_variable_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This function computes. More...

virtual void	make_assemblers_bdry_variable_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This function computes. More...

Other - make_ functions
virtual void	make_internal_cell_couplings ()
	This function fills out `internal_cell_couplings`. More...

virtual void	make_matrix_block_indices ()
	This function fills out `matrix_block_indices`. More...

virtual void	make_residual_indices ()
	This function fills out `residual_indices`. More...

Auxiliary classes
template<typename LAYER , typename INFO >
void	update_porosity (const LAYER *ptr, const INFO info, std::vector< double > &porosity)
	Inline function to obtain update the porosity for a given layer class. More...

template<typename LAYER , typename INFO >
void	update_permeability (const LAYER *ptr, const INFO info, std::vector< SymmetricTensor< 2, dim > > &permeability_INV, std::vector< SymmetricTensor< 2, dim > > &Forchheimer_permeability)
	Inline member function used to obtain the inverse permeability and the Forchheimer permeability for a given layer. More...

template<typename LAYER , typename INFO >
void	update_tortuosity (const LAYER *ptr, const INFO info, std::vector< SymmetricTensor< 2, dim > > &tortuosity)
	Inline member function used to obtain the tortuosity for a given layer. More...

template<typename LAYER >
void	update_gas_properties (const LAYER *ptr)
	Inline member function used to update. More...

template<typename LAYER >
void	update_inv_diffusion_coefficients (const LAYER *ptr, std::vector< Table< 2, SymmetricTensor< 2, dim > > > &inv_pDeff) const
	This private member function is used in make_assemblers_cell_variable_data in order to compute the inverse of the product of pressure and molecular diffusion coefficient. More...

template<typename LAYER >
void	update_partial_viscosities (const LAYER *ptr, const unsigned int &quadraturePoints, const std::vector< double > &porosity, const std::vector< std::vector< double > > &density, std::vector< std::vector< std::vector< double > > > &paramMatrix, std::vector< FullMatrix< double > > &PInv, std::vector< std::vector< double > > &partialViscosity, std::vector< std::vector< double > > &bulkViscosity) const
	This private member function is used to calculate the partial viscosity of the mixture and bulk viscosity, from dynamicViscosity, density, molar_mass. More...

template<typename LAYER >
void	update_delta_partial_viscosities (const LAYER *ptr, const std::vector< std::vector< double > > &partialViscosity, const std::vector< std::vector< std::vector< double > > > &paramMatrix, std::vector< FullMatrix< double > > &PInv, const std::vector< double > &porosity, const std::vector< std::vector< std::vector< double > > > &deltaDensity, const std::vector< std::vector< double > > &density, std::vector< std::vector< std::vector< double > > > &deltaPartialViscosity) const
	This private member function is used to calculate the variation in partial viscosity of the mixture. More...

template<typename LAYER >
void	update_delta_bulk_viscosities (const LAYER *ptr, const std::vector< std::vector< std::vector< double > > > &deltaPartialViscosity, std::vector< std::vector< std::vector< double > > > &deltaBulkViscosity) const
	Calls GasMixture function to loop through all variations of partial viscosity and calculates the varation in bulk viscosity according to bulk_viscosity_mode. More...

Protected Member Functions inherited from FuelCellShop::Equation::EquationBase< dim >
	EquationBase (FuelCell::SystemManagement &sys_management, boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData > data=boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >())
	Constructor. More...

virtual	~EquationBase ()
	Destructor. More...

virtual void	set_parameters (const std::vector< std::string > &name_dvar, const std::vector< double > &value_dvar, ParameterHandler &param)
	Set parameters using the parameter file, in order to run parametric/optimization studies. More...

virtual void	make_assemblers_generic_constant_data ()
	Function used to initialize variable information that will be needed to assemble matrix and residual and that will remain constant throughout the simulation. More...

void	select_cell_assemblers (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	This routine is used to select the make_assembly routines that need to be called inside assemble_cell_matrix to compute. More...

virtual void	make_internal_flux_couplings ()
	This function fills out `internal_flux_couplings` (DG FEM only) of a derived equation class. More...

virtual void	make_component_materialID_value ()
	This function fills out `component_materialID_value` of a derived equation class. More...

virtual void	make_component_boundaryID_value ()
	This function fills out `component_boundaryID_value` of a derived equation class. More...

virtual void	make_boundary_types ()
	This function fills out `boundary_types` of a derived equation class. More...

virtual void	make_multi_boundary_types ()
	This function fills out `multi_boundary_types` of a derived equation class. More...

virtual void	make_output_types ()
	This function fills out `output_types` of a derived equation class. More...

virtual void	make_multi_output_types ()
	This function fills out `multi_output_types` of a derived equation class. More...

virtual void	assemble_cell_Jacobian_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble the local Jacobian Matrix for Non-Linear problems. More...

virtual void	assemble_bdry_Jacobian_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local Jacobian boundary matrix for Non-Linear problems. More...

virtual void	assemble_cell_linear_matrix (FuelCell::ApplicationCore::MatrixVector &cell_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble the local cell matrix for Linear problems. More...

virtual void	assemble_cell_residual_rhs (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell RHS for nonlinear problems. More...

virtual void	assemble_cell_linear_rhs (FuelCell::ApplicationCore::FEVector &cell_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local cell RHS for Linear problems. More...

virtual void	assemble_bdry_linear_matrix (FuelCell::ApplicationCore::MatrixVector &bdry_matrices, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary matrix for linear problems. More...

virtual void	assemble_bdry_linear_rhs (FuelCell::ApplicationCore::FEVector &bdry_residual, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary RHS for linear problems. More...

void	standard_to_block_wise (FullMatrix< double > &target) const
	This function changes the order of dealii::FullMatrix<double> `target` from standard to block-wise. More...

void	standard_to_block_wise (Vector< double > &target) const
	This function changes the order of dealii::Vector<double> `target` from standard to block-wise. More...

void	dealII_to_appframe (FuelCell::ApplicationCore::MatrixVector &dst, const FullMatrix< double > &src, const std::vector< unsigned int > &matrix_block_indices) const
	This function converts the standard ordered structure dealii::FullMatrix<double> `src` into the block-wise ordered structure FuelCell::ApplicationCore::MatrixVector `dst`. More...

void	dealII_to_appframe (FuelCell::ApplicationCore::FEVector &dst, const Vector< double > &src, const std::vector< unsigned int > &residual_indices) const
	This function converts the standard ordered structure dealii::Vector<double> `src` into the block-wise ordered structure FuelCell::ApplicationCore::FEVector `dst`. More...

bool	belongs_to_boundary (const unsigned int &tria_boundary_id, const unsigned int &param_boundary_id) const
	This function returns `true` if a boundary indicator of an external face on the triangulation coincides with a boundary indicator defined in the parameters file of a derived equation class. More...

void	print_caller_name (const std::string &caller_name) const
	This function is used to print out the name of another function that has been declared in the scope of this class, but not yet been implemented. More...

Protected Attributes
Boolean constants and form of the drag force in porous media
std::vector< bool >	inertia_in_channels
	This object indicates whether the inertia term is ON or OFF in channels. More...

std::vector< bool >	shear_stress_in_channels
	This object indicates whether the shear stress term is ON or OFF in channels. More...

std::vector< bool >	gravity_in_channels
	This object indicates whether the gravity term is ON or OFF in channels. More...

std::vector< bool >	inertia_in_porous_media
	This object indicates whether the inertia term is ON or OFF in porous media. More...

std::vector< bool >	shear_stress_in_porous_media
	This object indicates whether the shear stress term is ON or OFF in porous media. More...

std::vector< bool >	gravity_in_porous_media
	This object indicates whether the gravity term is ON or OFF in porous media. More...

std::vector< std::string >	drag_in_porous_media
	This object indicates which form of the drag term is supposed to be chosen. More...

std::vector< bool >	normal_velocity_is_suppressed_weakly
	Sometimes we implement different types of slip boundary conditions on the curved impermeable walls of the domain or the walls that are not perfectly aligned with the coordinate axes. More...

Computational constants
unsigned int	n_species
	Number of species, . More...

bool	coupled_with_fuel_cell_physics

std::map< unsigned int, std::string >	gas_species_map
	Map of the gas species to their respective equation species number. More...

double	R_universal
	Universal gas constant, $R = 8.314462175 \cdot 10^7 \quad \left[ \frac{\text{g } \text{cm}^2}{\text{mol K } \text{sec}^2} \right]$ . More...

double	T_mixture
	Temperature of species mixture, $T_{\text{mixture}}^{\text{const}} \quad \left[ \text{K} \right]$ . More...

double	P_in
	Pressure at inlet, $P_{\text{in}}^{\text{const}} \quad \left[ \text{Pa} \right]$ . More...

Tensor< 1, dim >	gravity_acceleration
	Gravitational acceleration, $\mathbf{g} = \{ g_{\alpha} \}_{\alpha = 1}^d \quad \text{such that} \quad \forall \alpha \neq d : \quad g_{\alpha} = 0 \quad \left[ \frac{\text{cm}}{\text{sec}^2} \right] \quad \text{and} \quad g_d = -9.81 \cdot 10^2 \quad \left[ \frac{\text{cm}}{\text{sec}^2} \right]$ . More...

SymmetricTensor< 2, dim >	unit
	Unit tensor, $\hat{ \mathbf{I} } = \{ \delta_{\alpha \beta} \}_{\alpha,\beta = 1}^d$ . More...

std::vector< double >	molar_mass
	Molar mass of pure gas, $M_i \quad \left[ \frac{\text{g}}{\text{mol}} \right]$ . More...

std::vector< double >	dynamic_viscosity
	Dynamic viscosity of pure gas, $\mu^o_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ . More...

std::vector< double >	bulk_viscosity
	Bulk viscosity of pure gas, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ . More...

std::vector< double >	collision_diameter
	Collision diameter of pure gas, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ . More...

std::vector< double >	theta
	Navier slip coefficient of pure gas, $\theta_i$ . More...

std::vector< double >	eta
	Normal velocity suppression coefficient of pure gas, $\eta_i$ . More...

Table< 2, double >	maxwell_stefan_isobaric_diffusion_coefficient
	Each entry of this structure defines a Maxwell-Stefan isobaric diffusion coefficient of gas in gas , $\displaystyle \sum_{l=1}^N p_l \cdot \mathscr{D}_{ij} \quad \left[ \frac{\text{g cm}}{\text{sec}^3} \right]$ . More...

std::vector< double >	inlet_outlet_velocity_max
	Maximum inlet-outlet velocity of pure gas, $\mathbf{u}_{i, \text{in,out}}^{\text{max}}$ $\quad \left[ \frac{\text{cm}}{\text{sec}} \right]$ . More...

double	inlet_outlet_velocity_mixture_max
	Maximum inlet-outlet velocity of the mixture, $\mathbf{u}_{\text{mix,in,out}}^{\text{max}}$ $\quad \left[ \frac{\text{cm}}{\text{sec}} \right]$ . More...

bool	use_parabolic_profile

double	inlet_outlet_velocity_channel_base

double	inlet_outlet_velocity_channel_roof

int	inlet_outlet_boundary_ID

std::string	press_vel_comp_apply_to

std::string	inlet_outlet_velocity_mixture_equation

std::vector< double >	maxwell_constant
	These constants $\sigma_i$ are used in the Maxwell slip boundary condition. More...

Local CG FEM based assemblers - constant data (generic)
std::vector < FEValuesExtractors::Scalar >	density
	Density extractors. More...

std::vector < FEValuesExtractors::Vector >	velocity
	Velocity extractors. More...

Local CG FEM based assemblers - variable data (previous Newton iteration - cell)
Implementation is in the base class.
std::vector< std::vector < double > >	density_cell_old
	Density of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_density_cell_old
	Density gradient of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	velocity_cell_old
	Velocity of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < double > >	div_velocity_cell_old
	Velocity divergence of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	grads_velocity_cell_old
	Velocity symmetric gradient of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	mass_flux_cell_old
	Mass flux of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	momentum_flux_cell_old
	Momentum flux of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < double > >	pressure_cell_old
	Partial pressure of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	shear_stress_cell_old
	Shear stress of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < double > >	partial_viscosity_old
	Partial viscosity of mixture of each species, $\eta_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ , in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < double > >	bulk_viscosity_old
	Bulk viscosity of mixture of each species, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ . More...

std::vector< std::vector < std::vector< double > > >	paramMatrix_old
	paramMatrix is used for calculating partial viscosity of mixture in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< FullMatrix< double > >	PInv_old
	PInv_old is used for calculating the inverse of P when using the OmegaKG model for calculating partial viscosity in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	drag_cell_old
	Drag force of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	diffusion_cell_old
	Diffusion force of each species in the quadrature points of a cell at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	gravity_cell_old
	Gravity force of each species in the quadrature points of a cell at a previous Newton iteration. More...

Local CG FEM based assemblers - variable data (current Newton iteration - cell)
std::vector< std::vector < std::vector< double > > >	phi_density_cell
	Density shape functions. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	grad_phi_density_cell
	Density shape function gradients. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	phi_velocity_cell
	Velocity shape functions. More...

std::vector< std::vector < std::vector< double > > >	div_phi_velocity_cell
	Velocity shape function divergences. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	grads_phi_velocity_cell
	Velocity shape function symmetric gradients. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	delta_mass_flux_cell
	Mass flux perturbations. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	delta_momentum_flux_cell
	Momentum flux perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_pressure_cell
	Partial pressure perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_partial_viscosity_cell
	Partial dynamic viscosity perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_bulk_viscosity_cell
	Partial bulk viscosity perturbations. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	delta_shear_stress_cell
	Shear stress perturbations. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	delta_drag_cell
	Drag force perturbations. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	delta_diffusion_cell
	Diffusion force perturbations. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	delta_gravity_cell
	Gravity force perturbations. More...

Local CG FEM based assemblers - variable data (previous Newton iteration - boundary)
Implementation is in the base class.
std::vector< std::vector < double > >	density_bdry_old
	Density of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_density_bdry_old
	Density gradient of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	velocity_bdry_old
	Velocity of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < double > >	div_velocity_bdry_old
	Velocity divergence of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	grads_velocity_bdry_old
	Velocity symmetric gradient of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < Tensor< 1, dim > > >	mass_flux_bdry_old
	Mass flux of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	momentum_flux_bdry_old
	Momentum flux of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < double > >	pressure_bdry_old
	Partial pressure of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < SymmetricTensor< 2, dim > > >	shear_stress_bdry_old
	Shear stress of each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < double > >	partial_viscosity_bdry_old
	Partial dynamic viscosity, $\eta_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ , for each species in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< std::vector < double > >	bulk_viscosity_bdry_old
	Bulk viscosity of mixture of each species, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ . More...

std::vector< std::vector < std::vector< double > > >	paramMatrix_bdry_old
	paramMatrix is used for calculating partial viscosity of mixture in the quadrature points of a boundary at a previous Newton iteration. More...

std::vector< FullMatrix< double > >	PInv_bdry_old
	PInv_bdry_old is used for calculating the inverse of P when using the OmegaKG model for calculating partial viscosity in the quadrature points of a boundary at a previous Newton iteration. More...

Local CG FEM based assemblers - variable data (current Newton iteration - boundary)
std::vector< std::vector < std::vector< double > > >	phi_density_bdry
	Density shape functions. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	grad_phi_density_bdry
	Density shape function gradients. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	phi_velocity_bdry
	Velocity shape functions. More...

std::vector< std::vector < std::vector< double > > >	div_phi_velocity_bdry
	Velocity shape function divergences. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	grads_phi_velocity_bdry
	Velocity shape function symmetric gradients. More...

std::vector< std::vector < std::vector< Tensor< 1, dim > > > >	delta_mass_flux_bdry
	Mass flux perturbations. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	delta_momentum_flux_bdry
	Momentum flux perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_pressure_bdry
	Partial pressure perturbations. More...

std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	delta_shear_stress_bdry
	Shear stress perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_partial_viscosity_bdry
	Partial dyanmic viscosity perturbations. More...

std::vector< std::vector < std::vector< double > > >	delta_bulk_viscosity_bdry
	Partial bulk viscosity perturbations. More...

Local CG FEM based assemblers - variable data (other - boundary)
std::vector< std::vector < std::vector< SymmetricTensor < 2, dim > > > >	n_BY_phi_velocity_bdry_S
	Symmetrized tensor product of `normal_vectors` [ `q` ] and `phi_velocity_bdry` [ `s` ] [ `q` ] [ `k` ] in the quadrature points of a boundary. More...

Protected Attributes inherited from FuelCellShop::Equation::EquationBase< dim >
unsigned int	dofs_per_cell
	Number of degrees of freedom per cell. More...

unsigned int	n_q_points_cell
	Number of quadrature points per cell. More...

unsigned int	n_q_points_bdry
	Number of quadrature points per boundary. More...

DoFHandler< dim > ::active_cell_iterator	cell
	Currently active DoFHandler<dim> active cell iterator. More...

DoFHandler< dim > ::active_face_iterator	bdry
	Currently active DoFHandler<dim> active boundary iterator. More...

std::vector< double >	JxW_cell
	Jacobian of mapping by Weight in the quadrature points of a cell. More...

std::vector< double >	JxW_bdry
	Jacobian of mapping by Weight in the quadrature points of a boundary. More...

std::vector< Point< dim > >	normal_vectors
	Normal vectors in the quadrature points of a boundary. More...

std::vector< std::vector < Point< dim > > >	tangential_vectors
	Tangential vectors in the quadrature points of a boundary. More...

FuelCell::SystemManagement *	system_management
	Pointer to the external YourApplication<dim>::system_management object. More...

couplings_map	internal_cell_couplings
	This object contains the info on how the equations and solution variables of a derived equation class are coupled. More...

couplings_map	internal_flux_couplings
	This object contains the info on how the "X" and "Y" of a derived equation class are coupled (DG FEM only). More...

component_materialID_value_map	component_materialID_value
	This object reflects the following structure (see FuelCell::InitialAndBoundaryData namespace docs): More...

component_boundaryID_value_map	component_boundaryID_value
	This object reflects the following structure (see FuelCell::InitialAndBoundaryData namespace docs): More...

std::vector< BoundaryType >	boundary_types
	The list of boundary types of a derived equation class. More...

std::vector< std::vector < BoundaryType > >	multi_boundary_types
	The list of multiple boundary types of a derived equation class. More...

std::vector< OutputType >	output_types
	The list of output types of a derived equation class. More...

std::vector< std::vector < OutputType > >	multi_output_types
	The list of multiple output types of a derived equation class. More...

std::string	equation_name
	The name of a derived equation class. More...

std::string	name_base_variable
	Const std::string member storing name of the base solution variable corresponding to the equation represented by this class. More...

std::vector< unsigned int >	matrix_block_indices
	The system matrix block indices (a derived equation class) drawn from the global structure (a derived equation class + other active equation classes included into the computation). More...

std::vector< unsigned int >	residual_indices
	The residual indices (a derived equation class) drawn from the global structure (a derived equation class + other active equation classes included into the computation). More...

std::vector< bool >	counter
	This vector contains the collection of internal "counters" used by the derived equation classes. More...

EquationFlags	assemble_flags
	This vector contains a collection of internal flags to tell derived equation classes what needs to be re-computed. More...

boost::shared_ptr < FuelCell::ApplicationCore::ApplicationData >	data
	Data object for the application data to be passed to the equation classes. More...

std::string	solution_vector_name
	The name of the solution vector in FEVectors. More...

std::string	residual_vector_name
	The name of the residual vector name in FEVectors. More...

Additional Inherited Members
Public Attributes inherited from FuelCellShop::Equation::EquationBase< dim >
bool	variable_initial_data
	`true`, if variable initial data is prescribed on a part of the domain. More...

bool	variable_boundary_data
	`true`, if variable Dirichlet boundary conditions are prescribed on a part of the boundary. More...

Detailed Description

template<int dim>
class FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >

This class implements the multi-component mass transport equations proposed by Kerkhof-Geboers for fluid transport.

These equations are

steady-state,
compressible,
isothermal,
single-phase,
multi-component,

They take the following form:

point-wise form in the channels of fuel cells,
appropriately averaged over a so-called Representative Elementary Volume (REV) in the porous media regions,
solved with respect to point-wise $\{ \left( \rho_i, \mathbf{u}_i \right) \}_{i=1}^N$ in channels and with respect to REV-wise $\{ \left( < \rho_i >, < \mathbf{u}_i >^{\text{f}} \right) \}_{i=1}^N$ in porous media,
coupled with fuel cell physics in ReactionSourceTerms and SorptionSourceTerms classes.

For any species $ i = 1,N $ $\quad$ these equations can be written as

$\nabla \cdot \mathbf{F}_{ mass_i } = 0 \quad \text{in} \quad \Omega$ $\quad - \quad$ $ i $ -th mass conservation equation

$\nabla \cdot \hat{ \mathbf{F} }_{ mom_i } = \nabla \cdot \left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) + \left( \mathbf{F}_i + \mathbf{D}_i + \rho_i \mathbf{g} \right) \quad \text{in} \quad \Omega$ $\quad - \quad$ $ i $ -th momentum conservation equation

where

$\mathbf{F}_{ mass_i } = \rho_i \mathbf{u}_i$ $\quad - \quad$ $ i $ -th mass flux

$\hat{ \mathbf{F} }_{ mom_i } = \rho_i \mathbf{u}_i \otimes \mathbf{u}_i$ $\quad - \quad$ $ i $ -th momentum flux

$p_i = \rho_i \frac{R}{M_i} T_{\text{mixture}}^{\text{const}}$ $\quad - \quad$ $ i $ -th partial pressure

$\hat{ \boldsymbol\sigma }_i = 2 \mu_i \nabla_s \epsilon \mathbf{u}_i + \lambda_i \left( \nabla \cdot \epsilon \mathbf{u}_i \right) \hat{ \mathbf{I} }$ $\quad - \quad$ $ i $ -th shear stress

$\mathbf{F}_i = \begin{cases} \mathbf{0} \quad \text{in} \quad \Omega_c \\ - \mu_i \hat{ \mathbf{K} }^{-1} \epsilon \mathbf{u}_i - \hat{\boldsymbol\beta} \rho_i \big| \epsilon \mathbf{u}_i \big| \epsilon \mathbf{u}_i \quad \text{in} \quad \Omega_p \end{cases}$ $\quad - \quad$ $ i $ -th drag force

$\mathbf{D}_i = \displaystyle \sum_{j=1}^N p_i p_j \hat{ \mathbf{D} }_{ij}^{-1} \left( \epsilon \mathbf{u}_j - \epsilon \mathbf{u}_i \right)$ $\quad - \quad$ $ i $ -th diffusion force

$\hat{ \mathbf{D} }_{ij}^{-1} = \begin{cases} \displaystyle \left( \sum_{l=1}^N p_l \cdot \mathscr{D}_{ij} \right)^{-1} \hat{ \mathbf{I} } \quad \text{in} \quad \Omega_c \\ \displaystyle \left( \epsilon \sum_{l=1}^N p_l \cdot \mathscr{D}_{ij} \right)^{-1} \hat{ \mathbf{T} } \quad \text{in} \quad \Omega_p \end{cases}$ $\quad - \quad$ the inverse of $ i $ -th, $ j $ -th Maxwell–Stefan isobaric diffusion coefficient

To be well-posed, these equations are equipped with appropriate boundary conditions. Below we consider several types of boundaries and several types of boundary conditions assigned to those boundaries (here $ k $ denotes some portion of a boundary of a certain type).

Impermeable walls $\left( \Gamma^{\text{walls},k}_i \right)$ $\quad - \quad$ no-slip boundary condition

$\quad \mathbf{u}_i \Bigg|_{\Gamma^{\text{walls},k}_i} = \mathbf{0} \quad \text{OR}$

Impermeable walls $\left( \Gamma^{\text{walls},k}_i \right)$ $\quad - \quad$ Navier slip boundary condition

$\mathbf{u}_i \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{and} \quad \left(1-\theta_i \right) \mathbf{u}_i \cdot \boldsymbol\tau_{\alpha} + \theta_i \left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{with} \quad \alpha = 1, d-1 \quad \text{and} \quad 0 < \theta_i < 1 \quad \text{OR}$

Impermeable walls $\left( \Gamma^{\text{walls},k}_i \right)$ $\quad - \quad$ Maxwell slip boundary condition

$\mathbf{u}_i \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{and} \quad \mathbf{u}_i \cdot \boldsymbol\tau_{\alpha} + \frac{2-\sigma_i}{\sigma_i \rho_i} \sqrt{\frac{\pi M_i}{2RT_{\text{mixture}}^{\text{const}}}} \left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{with} \quad \alpha = 1, d-1 \quad \text{OR}$

Impermeable walls $\left( \Gamma^{\text{walls},k}_i \right)$ $\quad - \quad$ perfect slip boundary condition

$\mathbf{u}_i \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{and} \quad \left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{walls},k}_i} = 0 \quad \text{with} \quad \alpha = 1, d-1$

Symmetry line or plane $\left( \Gamma^{\text{sym}} \right)$ $\quad - \quad$ perfect slip boundary condition

$\forall i = 1,N: \quad \mathbf{u}_i \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{sym}}} = 0 \quad \text{and} \quad \left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{sym}}} = 0 \quad \text{with} \quad \alpha = 1, d-1$

Inlet-Outlet $\left( \Gamma^{\text{in-out},k}_i \right)$ $\quad - \quad$ Dirichlet boundary condition

$\rho_i \Bigg|_{\Gamma^{\text{in-out},k}_i} = \rho_i^{\text{prescribed},k} \quad \text{or} \quad \mathbf{u}_i \Bigg|_{\Gamma^{\text{in-out},k}_i} = \mathbf{u}_i^{\text{prescribed},k} \quad \text{or} \quad \text{both} \quad \text{OR/AND}$

Inlet-Outlet $\left( \Gamma^{\text{in-out},k}_i \right)$ $\quad - \quad$ normal stress free boundary condition

$\left( -p_i \hat{\boldsymbol{I}} + \hat{ \boldsymbol\sigma }_i \right) \mathbf{n} \Bigg|_{\Gamma^{\text{in-out},k}_i} = \mathbf{0} \quad \text{OR}$

Inlet-Outlet $\left( \Gamma^{\text{in-out},k}_i \right)$ $\quad - \quad$ normal shear stress free boundary condition

$\hat{ \boldsymbol\sigma }_i \mathbf{n} \Bigg|_{\Gamma^{\text{in-out},k}_i} = \mathbf{0}$

All these boundaries and boundary conditions can be specified in the parameters file as follows:

* Impermeable walls [species] = [boundary_id]: [type]

*

where

[species] = 1,2,3,4,5
[boundary_id] = 0,1,2,3,...
[type] = no-slip | Navier slip | Maxwell slip | perfect slip

* Symmetry line or plane [species] = [boundary_id]: [type]

*

where

[species] = 1,2,3,4,5
[boundary_id] = 0,1,2,3,...
[type] = perfect slip

* Inlet-Outlet [species] = [boundary_id]: [type]

*

where

[species] = 1,2,3,4,5
[boundary_id] = 0,1,2,3,...
[type] = Dirichlet density | Dirichlet density and normal stress free | Dirichlet density and normal shear stress free | Dirichlet velocity | Dirichlet density and velocity | normal stress free | normal shear stress free

These equations utilize

Channel,
GasDiffusionLayer,
MicroPorousLayer,
CatalystLayer

as layer classes and

GasMixture,
PureGas

as material classes and have the following output:

densities, $\rho_i$ $\quad \left[ \frac{\text{g}}{\text{cm}^3} \right]$
velocities, $\mathbf{u}_i$ $\quad \left[ \frac{\text{cm}}{\text{sec}} \right]$

We usually do not solve these equations in the membranes of fuel cells which is fully justified under the normal conditions of operation.

The whole problem is solved by linearizing the governing equations at each Newton iteration with subsequent CG FEM discretization in space.

The implementation is performed by means of using only one weak formulation for all $N \left( d + 1 \right)$ scalar governing equations. This approach guarantees the dim-independent programming of the equations at hand.

Note: outer_product() is a deal.ii function

Author: Valentin N. Zingan, Chad Balen and Marc Secanell, 2013-15

Constructor & Destructor Documentation

template<int dim>

FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::CompressibleMultiComponentKGEquationsCoupled	(	FuelCell::SystemManagement &	system_management,
		boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >	data = `boost::shared_ptr< FuelCell::ApplicationCore::ApplicationData >()`
	)

Constructor.

template<int dim>

virtual FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::~CompressibleMultiComponentKGEquationsCoupled ( )

virtual

Destructor.

Member Function Documentation

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::assemble_bdry_matrix	(	FuelCell::ApplicationCore::MatrixVector &	bdry_matrices,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &	bdry_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local boundary matrix.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::assemble_bdry_residual	(	FuelCell::ApplicationCore::FEVector &	bdry_residual,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &	bdry_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local boundary residual.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::assemble_cell_matrix	(	FuelCell::ApplicationCore::MatrixVector &	cell_matrices,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local cell matrix.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::assemble_cell_residual	(	FuelCell::ApplicationCore::FEVector &	cell_residual,
		const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

virtual

Assemble local cell residual.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::declare_parameters ( ParameterHandler & param ) const

virtual

Declare parameters.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

const std::map<unsigned int, std::string> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_gas_species_map ( ) const

inline

get_gas_species_map() returns a map relating the different KG species equations to the desired gas species being simulated; e.g 1:oxygen, 2:water vapour, 3:nitrogen means that the first 3 KG equations (Mass Cons., Mom.

Cons. X, Mom. Cons. Y) are for species oxygen, the next three are for water vapour, and the final three are for nitrogen.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gas_species_map.

template<int dim>

const int FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_boundary_ID ( ) const

inline

This function tells the application the boundary id to apply velocity profile equation to.

TODO: in the future it might be nice if OpenFCST could detect this based on boundary conditions

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_boundary_ID.

template<int dim>

const double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_channel_base ( ) const

inline

This function tells the application the height [cm] of the base of the channel with respect to origin.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_channel_base.

template<int dim>

const double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_channel_roof ( ) const

inline

This function tells the application the height [cm] of the roof of the channel with respect to origin.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_channel_roof.

template<int dim>

const std::vector<double>& FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_max ( ) const

inline

This function returns inlet_outlet_velocity_max.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_max.

template<int dim>

const std::string FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_mixture_equation ( ) const

inline

If get_use_parabolic_profile() is false then user can specify an equation to use for velocity profile at boundary.

Ex. inlet-outlet velocity of the mixture equation = -625*y*y + 66.25*y - 0.755625

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_mixture_equation.

template<int dim>

const double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_mixture_max ( ) const

inline

This function returns inlet_outlet_velocity_mixture_max.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_mixture_max.

template<int dim>

const unsigned int FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_num_of_species ( ) const

inline

If returns the number of species to use in the parameter file.

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_species.

template<int dim>

const std::string FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_press_vel_comp_apply_to ( ) const

inline

Outputs which component to apply variable boundary equation to (i.e.

Pressure, VelocityX, VelocityY, VelocityZ).

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::press_vel_comp_apply_to.

template<int dim>

const bool FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_use_parabolic_profile ( ) const

inline

This function tells the application if the user wishes to use a parabolic profile for a boundary condition.

If false then user must specify equation to use with parameter inlet-outlet velocity of the mixture equation

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::use_parabolic_profile.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::initialize ( ParameterHandler & param )

virtual

Initialize parameters.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_assemblers_bdry_constant_data ( const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo & bdry_info )

protectedvirtual

This function computes Local CG FEM based assemblers - constant data (boundary) and allocates the memory for.

Local CG FEM based assemblers - variable data (previous Newton iteration - boundary),
Local CG FEM based assemblers - variable data (current Newton iteration - boundary),
Local CG FEM based assemblers - variable data (other - boundary).

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_assemblers_bdry_variable_data	(	const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &	bdry_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

protectedvirtual

This function computes.

Local CG FEM based assemblers - variable data (previous Newton iteration - boundary),
Local CG FEM based assemblers - variable data (current Newton iteration - boundary),
Local CG FEM based assemblers - variable data (other - boundary).

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_assemblers_cell_constant_data ( const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo & cell_info )

protectedvirtual

This function computes Local CG FEM based assemblers - constant data (cell) and allocates the memory for.

Local CG FEM based assemblers - variable data (previous Newton iteration - cell),
Local CG FEM based assemblers - variable data (current Newton iteration - cell),
Local CG FEM based assemblers - variable data (other - cell).

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_assemblers_cell_variable_data	(	const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &	cell_info,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

protectedvirtual

This function computes.

Local CG FEM based assemblers - variable data (previous Newton iteration - cell),
Local CG FEM based assemblers - variable data (current Newton iteration - cell),
Local CG FEM based assemblers - variable data (other - cell).

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

template<typename INFO >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_assemblers_generic_constant_data	(	const INFO &	InFo,
		FuelCellShop::Layer::BaseLayer< dim > *const	layer
	)

protected

This function computes Computational constants and Local CG FEM based assemblers - constant data (generic).

The template parameter INFO is either typename FuelCell::ApplicationCore::DoFApplication<dim>::CellInfo or typename FuelCell::ApplicationCore::DoFApplication<dim>::FaceInfo.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_internal_cell_couplings ( )

protectedvirtual

This function fills out internal_cell_couplings.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_matrix_block_indices ( )

protectedvirtual

This function fills out matrix_block_indices.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::make_residual_indices ( )

protectedvirtual

This function fills out residual_indices.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

virtual void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::print_equation_info ( ) const

virtual

This function prints out the equations info.

Reimplemented from FuelCellShop::Equation::EquationBase< dim >.

template<int dim>

template<typename LAYER >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_bulk_viscosities	(	const LAYER *	ptr,
		const std::vector< std::vector< std::vector< double > > > &	deltaPartialViscosity,
		std::vector< std::vector< std::vector< double > > > &	deltaBulkViscosity
	)		const

inlineprotected

Calls GasMixture function to loop through all variations of partial viscosity and calculates the varation in bulk viscosity according to bulk_viscosity_mode.

All vectors must be sized correctly before using this function.

template<int dim>

template<typename LAYER >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities	(	const LAYER *	ptr,
		const std::vector< std::vector< double > > &	partialViscosity,
		const std::vector< std::vector< std::vector< double > > > &	paramMatrix,
		std::vector< FullMatrix< double > > &	PInv,
		const std::vector< double > &	porosity,
		const std::vector< std::vector< std::vector< double > > > &	deltaDensity,
		const std::vector< std::vector< double > > &	density,
		std::vector< std::vector< std::vector< double > > > &	deltaPartialViscosity
	)		const

inlineprotected

This private member function is used to calculate the variation in partial viscosity of the mixture.

Parameters:

Parameters

prt	- Pointer to the layer we would like to compute the coefficient for
partialViscosity	- vector of vectors of partial viscosity of mixture; first indice is quadrature point, second is species; [g/cm*s]
paramMatrix	- vector of vector of vectors used in calculation of partialViscosity; first indice is quadrature point, second is species 1 and second is species 2
porosity	- porosity in cell, vector of quadrature points
deltaDensity	- variation in density; same unit standard as density
density	- vector of vectors of density; first indice is species and second is quadrature point; [g/cm^3]
deltaPartialViscosity	- vector returned by reference contains variation of partial viscosity; first indice is species, second is quadrature point, and third is dof

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::collision_diameter, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::density, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::dynamic_viscosity, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::molar_mass, and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::T_mixture.

template<int dim>

template<typename LAYER >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties ( const LAYER * ptr )

inlineprotected

Inline member function used to update.

temperature,
molar_mass,
dynamic_viscosity,
maxwell_stefan_isobaric_diffusion_coefficient

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::collision_diameter, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::dynamic_viscosity, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::maxwell_stefan_isobaric_diffusion_coefficient, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::molar_mass, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_species, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::P_in, and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::T_mixture.

template<int dim>

template<typename LAYER >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_inv_diffusion_coefficients	(	const LAYER *	ptr,
		std::vector< Table< 2, SymmetricTensor< 2, dim > > > &	inv_pDeff
	)		const

inlineprotected

This private member function is used in make_assemblers_cell_variable_data in order to compute the inverse of the product of pressure and molecular diffusion coefficient.

This value is only a function of temperature.

Parameters:

prt: Pointer to the layer we would like to compute the coefficient for
inv_pDeff: returned value for the coefficient. The vector is re-initialized in the class, so an empty vector can be provided. It will be re-sized and filled as appropriate.

Warning: This routine still needs work...

References Units::C_UNIT2, Units::convert(), FuelCellShop::Equation::EquationBase< dim >::n_q_points_cell, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_species, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::P_in, and Units::UNIT2.

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template<int dim>

template<typename LAYER >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities	(	const LAYER *	ptr,
		const unsigned int &	quadraturePoints,
		const std::vector< double > &	porosity,
		const std::vector< std::vector< double > > &	density,
		std::vector< std::vector< std::vector< double > > > &	paramMatrix,
		std::vector< FullMatrix< double > > &	PInv,
		std::vector< std::vector< double > > &	partialViscosity,
		std::vector< std::vector< double > > &	bulkViscosity
	)		const

inlineprotected

This private member function is used to calculate the partial viscosity of the mixture and bulk viscosity, from dynamicViscosity, density, molar_mass.

As well, it returns paramMatrix for possible later calculations (like when calculating the variation). Since this function is used by make_assemblers_cell_variable_data and make_assemblers_bdry_variable_data which have different quadrature points one of the members is the number of quadrature points. NOTE: no need to size vectors paramMatrix, PInv, partialViscosity, and bulkViscosity sizing is done by this function.

Parameters:

Parameters

prt	- Pointer to the layer we would like to compute the coefficient for
quadraturePoints	- number of quadrature points in cell/boundary
porosity	- porosity in cell, vector of quadrature points
density	- vector of vectors of density; first indice is species and second is quadrature point; [g/cm^3]
paramMatrix	- used internally; vector of vector of vectors used in calculation of partialViscosity; first indice is quadrature point, second is species 1 and second is species 2
PInv	- used internally; this parameter provides the inverse of P for the calculation of OmegaKG viscosity and variation of,
partialViscosity	- vector of vectors of partial viscosity of mixture; first indice is quadrature point, second is species; [g/cm*s]
bulkViscosity,:	- vector of vectors of bulk viscosities; first indice is quadrature point, second is species; [g/cm*s]

References FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::collision_diameter, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::density, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::dynamic_viscosity, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::molar_mass, FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_species, and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::T_mixture.

template<int dim>

template<typename LAYER , typename INFO >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_permeability	(	const LAYER *	ptr,
		const INFO	info,
		std::vector< SymmetricTensor< 2, dim > > &	permeability_INV,
		std::vector< SymmetricTensor< 2, dim > > &	Forchheimer_permeability
	)

inlineprotected

Inline member function used to obtain the inverse permeability and the Forchheimer permeability for a given layer.

Note

The pointer should be of type:

FuelCellShop::Layer::GasDiffusionLayer<dim>
FuelCellShop::Layer::MicroPorousLayer<dim>
FuelCellShop::Layer::CatalystLayer<dim>
FuelCellShop::Layer::ExperimentalPorousLayer<dim>

template<int dim>

template<typename LAYER , typename INFO >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_porosity	(	const LAYER *	ptr,
		const INFO	info,
		std::vector< double > &	porosity
	)

inlineprotected

Inline function to obtain update the porosity for a given layer class.

Note

The pointer should be of type:

FuelCellShop::Layer::GasDiffusionLayer<dim>
FuelCellShop::Layer::MicroPorousLayer<dim>
FuelCellShop::Layer::CatalystLayer<dim>
FuelCellShop::Layer::ExperimentalPorousLayer<dim>

template<int dim>

template<typename LAYER , typename INFO >

void FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_tortuosity	(	const LAYER *	ptr,
		const INFO	info,
		std::vector< SymmetricTensor< 2, dim > > &	tortuosity
	)

inlineprotected

Inline member function used to obtain the tortuosity for a given layer.

Note

The pointer should be of type:

FuelCellShop::Layer::GasDiffusionLayer<dim>
FuelCellShop::Layer::MicroPorousLayer<dim>
FuelCellShop::Layer::CatalystLayer<dim>
FuelCellShop::Layer::ExperimentalPorousLayer<dim>

Member Data Documentation

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::bulk_viscosity

protected

Bulk viscosity of pure gas, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ .

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::bulk_viscosity_bdry_old

protected

Bulk viscosity of mixture of each species, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ .

in the quadrature points of a boundary at a previous Newton iteration. NOTE: first index is the quadrature point and second index is the species.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::bulk_viscosity_old

protected

Bulk viscosity of mixture of each species, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ .

in the quadrature points of a cell at a previous Newton iteration. NOTE: first index is the quadrature point and second index is the species.

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::collision_diameter

protected

Collision diameter of pure gas, $\lambda_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

bool FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::coupled_with_fuel_cell_physics

protected

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_bulk_viscosity_bdry

protected

Partial bulk viscosity perturbations.

delta_viscosity_mix_bdry [ s ] [ q ] [ k ] denotes $ k $ -th partial bulk viscosity perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_bulk_viscosity_cell

protected

Partial bulk viscosity perturbations.

delta_bulk_viscosity_cell [ s ] [ q ] [ k ] denotes $ k $ -th partial bulk velocity perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_diffusion_cell

protected

Diffusion force perturbations.

delta_diffusion_cell [ s ] [ q ] [ k ] denotes $ k $ -th diffusion force perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_drag_cell

protected

Drag force perturbations.

delta_drag_cell [ s ] [ q ] [ k ] denotes $ k $ -th drag force perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_gravity_cell

protected

Gravity force perturbations.

delta_gravity_cell [ s ] [ q ] [ k ] denotes $ k $ -th gravity force perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_mass_flux_bdry

protected

Mass flux perturbations.

delta_mass_flux_bdry [ s ] [ q ] [ k ] denotes $ k $ -th mass flux perturbation computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_mass_flux_cell

protected

Mass flux perturbations.

delta_mass_flux_cell [ s ] [ q ] [ k ] denotes $ k $ -th mass flux perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_momentum_flux_bdry

protected

Momentum flux perturbations.

delta_momentum_flux_bdry [ s ] [ q ] [ k ] denotes $ k $ -th momentum flux perturbation computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_momentum_flux_cell

protected

Momentum flux perturbations.

delta_momentum_flux_cell [ s ] [ q ] [ k ] denotes $ k $ -th momentum flux perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_partial_viscosity_bdry

protected

Partial dyanmic viscosity perturbations.

delta_viscosity_mix_bdry [ s ] [ q ] [ k ] denotes $ k $ -th partial dyanmic viscosity perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_partial_viscosity_cell

protected

Partial dynamic viscosity perturbations.

delta_partial_viscosity_cell [ s ] [ q ] [ k ] denotes $ k $ -th partial dynamic velocity perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_pressure_bdry

protected

Partial pressure perturbations.

delta_pressure_bdry [ s ] [ q ] [ k ] denotes $ k $ -th partial pressure perturbation computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_pressure_cell

protected

Partial pressure perturbations.

delta_pressure_cell [ s ] [ q ] [ k ] denotes $ k $ -th partial pressure perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_shear_stress_bdry

protected

Shear stress perturbations.

delta_shear_stress_bdry [ s ] [ q ] [ k ] denotes $ k $ -th shear stress perturbation computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::delta_shear_stress_cell

protected

Shear stress perturbations.

delta_shear_stress_cell [ s ] [ q ] [ k ] denotes $ k $ -th shear stress perturbation computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< FEValuesExtractors::Scalar > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::density

protected

Density extractors.

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::density_bdry_old

protected

Density of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::density_cell_old

protected

Density of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::diffusion_cell_old

protected

Diffusion force of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::div_phi_velocity_bdry

protected

Velocity shape function divergences.

div_phi_velocity_bdry [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function divergence computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::div_phi_velocity_cell

protected

Velocity shape function divergences.

div_phi_velocity_cell [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function divergence computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::div_velocity_bdry_old

protected

Velocity divergence of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::div_velocity_cell_old

protected

Velocity divergence of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::drag_cell_old

protected

Drag force of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector<std::string> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::drag_in_porous_media

protected

This object indicates which form of the drag term $ i $ is supposed to be chosen.

There are four options currently implemented in FCST. These options are

none,
Darcy,
Forchheimer,
Forchheimer modified.

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::dynamic_viscosity

protected

Dynamic viscosity of pure gas, $\mu^o_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::eta

protected

Normal velocity suppression coefficient of pure gas, $\eta_i$ .

template<int dim>

std::map<unsigned int, std::string> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gas_species_map

protected

Map of the gas species to their respective equation species number.

Possible names for gasses include: oxygen, water, nitrogen. $ N $ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_gas_species_map().

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grad_density_bdry_old

protected

Density gradient of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grad_density_cell_old

protected

Density gradient of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grad_phi_density_bdry

protected

Density shape function gradients.

grad_phi_density_bdry [ s ] [ q ] [ k ] denotes $ k $ -th density shape function gradient computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grad_phi_density_cell

protected

Density shape function gradients.

grad_phi_density_cell [ s ] [ q ] [ k ] denotes $ k $ -th density shape function gradient computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grads_phi_velocity_bdry

protected

Velocity shape function symmetric gradients.

grads_phi_velocity_bdry [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function symmetric gradient computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grads_phi_velocity_cell

protected

Velocity shape function symmetric gradients.

grads_phi_velocity_cell [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function symmetric gradient computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grads_velocity_bdry_old

protected

Velocity symmetric gradient of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::grads_velocity_cell_old

protected

Velocity symmetric gradient of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

Tensor<1,dim> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gravity_acceleration

protected

Gravitational acceleration, $\mathbf{g} = \{ g_{\alpha} \}_{\alpha = 1}^d \quad \text{such that} \quad \forall \alpha \neq d : \quad g_{\alpha} = 0 \quad \left[ \frac{\text{cm}}{\text{sec}^2} \right] \quad \text{and} \quad g_d = -9.81 \cdot 10^2 \quad \left[ \frac{\text{cm}}{\text{sec}^2} \right]$ .

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gravity_cell_old

protected

Gravity force of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gravity_in_channels

protected

This object indicates whether the gravity term $ i $ is ON or OFF in channels.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::gravity_in_porous_media

protected

This object indicates whether the gravity term $ i $ is ON or OFF in porous media.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inertia_in_channels

protected

This object indicates whether the inertia term $ i $ is ON or OFF in channels.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inertia_in_porous_media

protected

This object indicates whether the inertia term $ i $ is ON or OFF in porous media.

template<int dim>

int FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_boundary_ID

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_boundary_ID().

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_channel_base

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_channel_base().

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_channel_roof

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_channel_roof().

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_max

protected

Maximum inlet-outlet velocity of pure gas, $\mathbf{u}_{i, \text{in,out}}^{\text{max}}$ $\quad \left[ \frac{\text{cm}}{\text{sec}} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_max().

template<int dim>

std::string FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_mixture_equation

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_mixture_equation().

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::inlet_outlet_velocity_mixture_max

protected

Maximum inlet-outlet velocity of the mixture, $\mathbf{u}_{\text{mix,in,out}}^{\text{max}}$ $\quad \left[ \frac{\text{cm}}{\text{sec}} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_inlet_outlet_velocity_mixture_max().

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::mass_flux_bdry_old

protected

Mass flux of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::mass_flux_cell_old

protected

Mass flux of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::maxwell_constant

protected

These constants $\sigma_i$ are used in the Maxwell slip boundary condition.

template<int dim>

Table< 2, double > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::maxwell_stefan_isobaric_diffusion_coefficient

protected

Each entry of this structure defines a Maxwell-Stefan isobaric diffusion coefficient of gas $ i $ in gas $ j $ , $\displaystyle \sum_{l=1}^N p_l \cdot \mathscr{D}_{ij} \quad \left[ \frac{\text{g cm}}{\text{sec}^3} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties().

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::molar_mass

protected

Molar mass of pure gas, $M_i \quad \left[ \frac{\text{g}}{\text{mol}} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::momentum_flux_bdry_old

protected

Momentum flux of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::momentum_flux_cell_old

protected

Momentum flux of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector< std::vector< std::vector< SymmetricTensor<2,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_BY_phi_velocity_bdry_S

protected

Symmetrized tensor product of normal_vectors [ q ] and phi_velocity_bdry [ s ] [ q ] [ k ] in the quadrature points of a boundary.

template<int dim>

unsigned int FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::n_species

protected

Number of species, $ N $ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_num_of_species(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_inv_diffusion_coefficients(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::normal_velocity_is_suppressed_weakly

protected

Sometimes we implement different types of slip boundary conditions on the curved impermeable walls of the domain or the walls that are not perfectly aligned with the coordinate axes.

In this case, it might be quite problematic (but still possible) to strictly enforce the normal component of velocity $ i $ be equal to 0.

The alternative approach is doing that by introducing a penalization term $\displaystyle \int_{ \Gamma^{\text{walls},k}_i } \frac{1}{\eta_i} \left( \boldsymbol\omega_i \cdot \mathbf{n} \right) \left( \mathbf{u}_i \cdot \mathbf{n} \right) dS$ with $\eta_i \sim 10^{-10} - 10^{-12}$ into the weak formulation of the equations at hand.

This object indicates whether the penalty method is used.

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::P_in

protected

Pressure at inlet, $P_{\text{in}}^{\text{const}} \quad \left[ \text{Pa} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_inv_diffusion_coefficients().

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::paramMatrix_bdry_old

protected

paramMatrix is used for calculating partial viscosity of mixture in the quadrature points of a boundary at a previous Newton iteration.

NOTE: first index is the quadrature point and second and third indices are the species.

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::paramMatrix_old

protected

paramMatrix is used for calculating partial viscosity of mixture in the quadrature points of a cell at a previous Newton iteration.

NOTE: first index is the quadrature point and second and third indices are the species.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::partial_viscosity_bdry_old

protected

Partial dynamic viscosity, $\eta_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ , for each species in the quadrature points of a boundary at a previous Newton iteration.

NOTE: first index is the quadrature point and second index is the species.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::partial_viscosity_old

protected

Partial viscosity of mixture of each species, $\eta_i \quad \left[ \frac{\text{g}}{\text{cm sec}} \right]$ , in the quadrature points of a cell at a previous Newton iteration.

NOTE: first index is the quadrature point and second index is the species.

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::phi_density_bdry

protected

Density shape functions.

phi_density_bdry [ s ] [ q ] [ k ] denotes $ k $ -th density shape function computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector<double> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::phi_density_cell

protected

Density shape functions.

phi_density_cell [ s ] [ q ] [ k ] denotes $ k $ -th density shape function computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::phi_velocity_bdry

protected

Velocity shape functions.

phi_velocity_bdry [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function computed in $ q $ -th quadrature point of a boundary for species $ s $ .

template<int dim>

std::vector< std::vector< std::vector< Tensor<1,dim> > > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::phi_velocity_cell

protected

Velocity shape functions.

phi_velocity_cell [ s ] [ q ] [ k ] denotes $ k $ -th velocity shape function computed in $ q $ -th quadrature point of a cell for species $ s $ .

template<int dim>

std::vector< FullMatrix<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::PInv_bdry_old

protected

PInv_bdry_old is used for calculating the inverse of P when using the OmegaKG model for calculating partial viscosity in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< FullMatrix<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::PInv_old

protected

PInv_old is used for calculating the inverse of P when using the OmegaKG model for calculating partial viscosity in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::string FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::press_vel_comp_apply_to

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_press_vel_comp_apply_to().

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::pressure_bdry_old

protected

Partial pressure of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::pressure_cell_old

protected

Partial pressure of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::R_universal

protected

Universal gas constant, $R = 8.314462175 \cdot 10^7 \quad \left[ \frac{\text{g } \text{cm}^2}{\text{mol K } \text{sec}^2} \right]$ .

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::shear_stress_bdry_old

protected

Shear stress of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< SymmetricTensor<2,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::shear_stress_cell_old

protected

Shear stress of each species in the quadrature points of a cell at a previous Newton iteration.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::shear_stress_in_channels

protected

This object indicates whether the shear stress term $ i $ is ON or OFF in channels.

template<int dim>

std::vector<bool> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::shear_stress_in_porous_media

protected

This object indicates whether the shear stress term $ i $ is ON or OFF in porous media.

template<int dim>

double FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::T_mixture

protected

Temperature of species mixture, $T_{\text{mixture}}^{\text{const}} \quad \left[ \text{K} \right]$ .

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_delta_partial_viscosities(), FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_gas_properties(), and FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::update_partial_viscosities().

template<int dim>

std::vector<double> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::theta

protected

Navier slip coefficient of pure gas, $\theta_i$ .

template<int dim>

SymmetricTensor<2,dim> FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::unit

protected

Unit tensor, $\hat{ \mathbf{I} } = \{ \delta_{\alpha \beta} \}_{\alpha,\beta = 1}^d$ .

template<int dim>

bool FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::use_parabolic_profile

protected

Referenced by FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::get_use_parabolic_profile().

template<int dim>

std::vector< FEValuesExtractors::Vector > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::velocity

protected

Velocity extractors.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::velocity_bdry_old

protected

Velocity of each species in the quadrature points of a boundary at a previous Newton iteration.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >::velocity_cell_old

protected

Velocity of each species in the quadrature points of a cell at a previous Newton iteration.

The documentation for this class was generated from the following file:

compressible_multi_component_KG_equations_coupled.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

template<int dim> class FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<int dim>
class FuelCellShop::Equation::CompressibleMultiComponentKGEquationsCoupled< dim >