This class deals with Navier-Stokes fluid transport equations. More...

#include <incompressible_single_component_NS_equations.h>

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

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

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

virtual	~IncompressibleSingleComponentNSEquations ()
	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 double &	get_inlet_outlet_velocity_max () const
	This function returns `inlet_outlet_velocity_max`. More...

const std::string	get_inlet_outlet_equation () const
	User can specify an equation to use for density/velocity profile at boundary. More...

const unsigned int	get_inlet_outlet_boundary_ID () const
	Outputs the Boundary ID to apply Dirichlet velocity or Dirichlet pressure to. More...

const std::string	get_press_vel_comp_apply_to () const
	Outputs which equation to apply equation to (Pressure, VelocityX, VelocityY, VelocityZ). 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
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...

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...

virtual void	make_assemblers_cell_constant_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info)
	Function used to initialize cell speciific information that remains constant regardless of the cell being computed. More...

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

virtual void	make_assemblers_cell_variable_data (const typename FuelCell::ApplicationCore::DoFApplication< dim >::CellInfo &cell_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Function used to compute cell specific information such as shape functions, shape function gradients, solution at each quadrature point. More...

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

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
bool	inertia_in_channels
	This object indicates whether the inertia term is ON or OFF in channels. More...

bool	shear_stress_in_channels
	This object indicates whether the shear stress term is ON or OFF in channels. More...

bool	gravity_in_channels
	This object indicates whether the gravity term is ON or OFF in channels. More...

bool	inertia_in_porous_media
	This object indicates whether the inertia term is ON or OFF in porous media. More...

bool	shear_stress_in_porous_media
	This object indicates whether the shear stress term is ON or OFF in porous media. More...

bool	gravity_in_porous_media
	This object indicates whether the gravity term is ON or OFF in porous media. More...

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

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

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

double	theta
	Navier slip coefficient, $\theta$ . More...

double	eta
	Normal velocity suppression coefficient, $\eta$ . More...

double	inlet_outlet_velocity_max
	Maximum inlet-outlet velocity, $\mathbf{u}_{\text{in,out}}^{\text{max}}$ $\quad \left[ \frac{\text{m}}{\text{sec}} \right]$ . More...

std::string	inlet_outlet_equation

unsigned int	inlet_outlet_boundary_ID

std::string	press_vel_comp_apply_to

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::IncompressibleSingleComponentNSEquations< dim >

This class deals with Navier-Stokes fluid transport equations.

According to classification, these equations are

steady-state,
incompressible,
isothermal,
single-phase,
single-component,
supposed to take the 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 $\left( p, \mathbf{u} \right)$ in channels and with respect to REV-wise $\left( <p>, <\mathbf{u}> \right)$ in porous media.

These equations can be written as

$\nabla \cdot \mathbf{u} = 0 \quad \text{in} \quad \Omega$ $\quad - \quad$ mass conservation equation

$\rho \nabla \cdot \left( \frac{1}{\epsilon} \mathbf{u} \otimes \mathbf{u} \right) = \nabla \cdot \left( -p \hat{\mathbf{I}} + \hat{\boldsymbol\sigma} \right) + \left( \mathbf{F} + \epsilon \rho \mathbf{g} \right) \quad \text{in} \quad \Omega$ $\quad - \quad$ momentum conservation equation

where

$\hat{\boldsymbol\sigma} = 2 \mu \nabla_s \mathbf{u}$ $\quad - \quad$ shear stress

$\mathbf{F} = \begin{cases} \mathbf{0} \quad \text{in} \quad \Omega_c \\ - \mu \hat{ \mathbf{K} }^{-1} \mathbf{u} - \hat{\boldsymbol\beta} \rho \big| \mathbf{u} \big| \mathbf{u} \quad \text{in} \quad \Omega_p \end{cases}$ $\quad - \quad$ drag force

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

$\quad \mathbf{u} \Bigg|_{\Gamma^{\text{walls},k}} = \mathbf{0} \quad \text{OR}$
Impermeable walls $\left( \Gamma^{\text{walls},k} \right)$ $\quad - \quad$ Navier slip boundary condition

$\mathbf{u} \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{walls},k}} = 0 \quad \text{and} \quad \left(1-\theta \right) \mathbf{u} \cdot \boldsymbol\tau_{\alpha} + \theta \left( -p \hat{\mathbf{I}} + \hat{\boldsymbol\sigma} \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{walls},k}} = 0 \quad \text{with} \quad \alpha = 1, d-1 \quad \text{and} \quad 0 < \theta < 1 \quad \text{OR}$
Impermeable walls $\left( \Gamma^{\text{walls},k} \right)$ $\quad - \quad$ perfect slip boundary condition

$\mathbf{u} \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{walls},k}} = 0 \quad \text{and} \quad \left( -p \hat{\mathbf{I}} + \hat{\boldsymbol\sigma} \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{walls},k}} = 0 \quad \text{with} \quad \alpha = 1, d-1$
Symmetry line or plane $\left( \Gamma^{\text{sym}} \right)$ $\quad - \quad$ perfect slip boundary condition

$\mathbf{u} \cdot \mathbf{n} \Bigg|_{\Gamma^{\text{sym}}} = 0 \quad \text{and} \quad \left( -p \hat{\mathbf{I}} + \hat{\boldsymbol\sigma} \right) \mathbf{n} \cdot \boldsymbol\tau_{\alpha} \Bigg|_{\Gamma^{\text{sym}}} = 0 \quad \text{with} \quad \alpha = 1, d-1$
Inlet-Outlet $\left( \Gamma^{\text{in-out},k} \right)$ $\quad - \quad$ Dirichlet boundary condition

$p \Bigg|_{\Gamma^{\text{in-out},k}} = p^{\text{prescribed},k} \quad \text{or} \quad \mathbf{u} \Bigg|_{\Gamma^{\text{in-out},k}} = \mathbf{u}^{\text{prescribed},k} \quad \text{or} \quad \text{both} \quad \text{OR/AND}$
Inlet-Outlet $\left( \Gamma^{\text{in-out},k} \right)$ $\quad - \quad$ normal stress free boundary condition

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

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

* Impermeable walls = [boundary_id]: [type]

*

where

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

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

*

where

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

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

*

where

[boundary_id] = 0,1,2,3,...
[type] = Dirichlet pressure | Dirichlet pressure and normal stress free | Dirichlet velocity | Dirichlet pressure and velocity | normal stress free

These equations utilize

Channel,
ExperimentalPorousLayer

as layer classes and

ExperimentalFluid,
ExperimentalSolid

as material classes and have the following output:

pressure, $\quad \left[ \text{Pa} \right]$
velocity, $\mathbf{u}$ $\quad \left[ \frac{\text{m}}{\text{sec}} \right]$

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 $ d + 1 $ scalar governing equations. This approach guarantees the dim-independent programming of the equations at hand.

Author: Valentin N. Zingan, 2012

Constructor & Destructor Documentation

template<int dim>

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

Constructor.

template<int dim>

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

virtual

Destructor.

Member Function Documentation

template<int dim>

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

virtual

Declare parameters.

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

template<int dim>

const unsigned int FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::get_inlet_outlet_boundary_ID ( ) const

inline

Outputs the Boundary ID to apply Dirichlet velocity or Dirichlet pressure to.

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

template<int dim>

const std::string FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::get_inlet_outlet_equation ( ) const

inline

User can specify an equation to use for density/velocity profile at boundary.

E. inlet-outlet equation = -625*y*y + 66.25*y - 0.755625

References FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inlet_outlet_equation.

template<int dim>

const double& FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::get_inlet_outlet_velocity_max ( ) const

inline

This function returns inlet_outlet_velocity_max.

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

template<int dim>

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

inline

Outputs which equation to apply equation to (Pressure, VelocityX, VelocityY, VelocityZ).

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

template<int dim>

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

virtual

Initialize parameters.

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

template<int dim>

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

protectedvirtual

This function fills out residual_indices.

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

template<int dim>

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

virtual

This function prints out the equations info.

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

Member Data Documentation

template<int dim>

std::string FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::drag_in_porous_media

protected

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

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

none,
Darcy,
Forchheimer,
Forchheimer modified.

template<int dim>

double FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::eta

protected

Normal velocity suppression coefficient, $\eta$ .

template<int dim>

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

protected

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

template<int dim>

bool FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::gravity_in_channels

protected

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

template<int dim>

bool FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::gravity_in_porous_media

protected

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

template<int dim>

bool FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inertia_in_channels

protected

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

template<int dim>

bool FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inertia_in_porous_media

protected

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

template<int dim>

unsigned int FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inlet_outlet_boundary_ID

protected

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

template<int dim>

std::string FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inlet_outlet_equation

protected

Referenced by FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::get_inlet_outlet_equation().

template<int dim>

double FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< dim >::inlet_outlet_velocity_max

protected

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

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

template<int dim>

bool FuelCellShop::Equation::IncompressibleSingleComponentNSEquations< 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 be equal to 0.

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