This class implements a mass conservation equation for liquid transport in a fuel cell porous media. More...

#include <liquid_transport_equation.h>

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

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

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

virtual	~LiquidPressureEquation ()
	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_rhs, 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_rhs, const typename FuelCell::ApplicationCore::DoFApplication< dim >::FaceInfo &bdry_info, FuelCellShop::Layer::BaseLayer< dim > *const layer)
	Assemble local boundary residual. More...

Accessors and info
virtual void	print_equation_info () const
	The function prints out the equation's 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
virtual void	make_assemblers_generic_constant_data ()
	This function computes 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 `shape` `functions`, `shape` `function` `gradients`, and `JxW_cell` in Local CG FEM based assemblers - variable data (cell) . 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 `shape` `functions`, normal_vectors, and `JxW_bdry` in Local CG FEM based assemblers - variable data (boundary) . 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 Local CG FEM based assemblers - variable data (cell) . 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 Local CG FEM based assemblers - variable data (boundary) . More...

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

virtual void	make_boundary_types ()
	This function fills out `boundary_types`. More...

virtual void	make_output_types ()
	This function fills out `output_types`. 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...

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_multi_boundary_types ()
	This function fills out `multi_boundary_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	make_matrix_block_indices ()
	This function is only needed to provide the last argument to dealII_to_appframe. More...

virtual void	make_residual_indices ()
	This function is only needed to provide the last argument to dealII_to_appframe. 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
bool	cell_residual_counter
	Counter set to TRUE when `cell_residual` is being assembled. More...

unsigned int	last_iter_cell
	Variable used to store the index in cell_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute cell_matrix and cell_residual. More...

unsigned int	last_iter_bdry
	Variable used to store the index in bdry_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute bdry_matrix and bdry_residual. More...

bool	breakthrough_phenomenon
	This data member is set to true when the following boundary condition is to be applied at the boundary $N = k (p_{c(threshold)} - p_c)$ . More...

std::vector< bool >	reached_breakthrough_pressure
	Once the liquid pressure at the GDL and channel interface reaches the breakthrouhg pressure the following boundary condition is to set to be applied $N = k (p_{c(threshold)} - p_c)$ . More...

std::map< unsigned int, double >	capillary_pressure_current_flux_map
	The map is used as the parameter in $N = k_1 (p_{c(threshold)} - p_c)$ . More...

double	p_channel_GDL
	The boundary condition term which indicates the liquid pressure (Pa) $p_{c(threshold1)}$ in $N = k_1 (p_{c(threshold1)} - p_c)$ . More...

double	p_channel_GDL_second
	The boundary condition term which indicates the breakthrough liquid pressure (Pa). More...

double	temperature
	Temperature [in K] of the layer. More...

Generic Constant Data
VariableInfo	p_liquid_water
	VariableInfo structure corresponding to `"liquid_pressure"`. More...

VariableInfo	x_water
	VariableInfo structure corresponding to `"water_molar_fraction"`. More...

VariableInfo	t_rev
	VariableInfo structure corresponding to `"temperature_of_REV"`. More...

unsigned int	fickswater_blockindex_xwater
	Block index for `"water_molar_fraction"` corresponding to "Ficks Transport Equation - water". More...

unsigned int	fickswater_blockindex_pliquid
	Block index for `"liquid_pressure"` corresponding to "Ficks Transport Equation - water". More...

unsigned int	fickswater_blockindex_trev
	Block index for `"temperature_of_REV"` corresponding to "Ficks Transport Equation - water". More...

unsigned int	thermal_blockindex_xwater
	Block index for `"water_molar_fraction"` corresponding to "Thermal Transport Equation". More...

unsigned int	thermal_blockindex_pliquid
	Block index for `"liquid_pressure"` corresponding to "Thermal Transport Equation". More...

unsigned int	thermal_blockindex_trev
	Block index for `"temperature_of_REV"` corresponding to "Thermal Transport Equation". More...

double	M_water
	Molar weight of water in grams/mole. More...

double	rho_l
	Density of liquid water, $\rho_l ~\left[ \frac{g}{cm^3} \right]$ . More...

double	k_sat
	Saturated permeability inside the porous media, $k_{sat} ~\left[ cm^2 \right]$ . More...

double	k_sat_bdry
	Saturated permeability at the boundary of the domain, $k_{satbdry} ~\left[ cm^2 \right]$ . More...

Local CG FEM based assemblers - variable data (cell)
double	p_cell
	Total pressure $\left[ Pa \right]$ in the cell. More...

std::vector< Tensor< 2, dim > >	rhok_mu_cell
	$\frac{\rho_l \hat{k}_l}{\mu_l}$ , at all quadrature points in the cell. More...

std::vector< Tensor< 2, dim > >	rhok_mu_cell_bdry
	$\frac{\rho_l \hat{k}_l}{\mu_l}$ , at all quadrature points in the boundary. More...

std::vector< Tensor< 2, dim > >	rho_mu_dk_dp_cell
	Computing the derivitive with respect to in the function $\frac{\rho_l \hat{k}_l(p_c)}{\mu_l(T)}$ , at all quadrature points in the cell. More...

std::vector< Tensor< 2, dim > >	dT_rhok_mu_cell
	Computing the derivitive with respect to in the function $\frac{\rho_l \hat{k}_l(p_c)}{\mu_l(T)}$ , at all quadrature points in the cell. More...

std::vector< std::vector < double > >	phi_p_cell
	$\mathbf{p_c}$ shape functions. More...

std::vector< std::vector < double > >	phi_p_cell_bdry
	$\mathbf{p_c}$ shape functions at the boundary. More...

std::vector< std::vector < double > >	phi_xwater_cell
	$\mathbf{x_{H_2O}}$ shape functions. More...

std::vector< std::vector < double > >	phi_T_cell
	$\mathbf{T}$ shape functions. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_p_cell
	$\mathbf{p_c}$ shape function gradients. More...

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_T_cell
	$\mathbf{T}$ shape function gradients. 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::LiquidPressureEquation< dim >

This class implements a mass conservation equation for liquid transport in a fuel cell porous media.

The liquid water velocity is based on Darcy's law.

Governing equation

The governing equation is based on a mass balance combined with Darcy's law. The equation is given by:

$\qquad -\mathbf{\nabla} \cdot \left[ \frac{\rho_l \hat{k}_l}{\mu_l} \mathbf{\nabla} p_c \right] = 0 \quad \in \quad \Omega$ where

$\rho_l$ is liquid density $\left[ \frac{g}{cm^3}\right]$ .
$\hat{k}_l$ is liquid permeability tensor $\left[ cm^2 \right]$ , which can be a function of liquid_pressure, .
$\mu_l$ is liquid viscosity $\left[ \frac{g}{cm \cdot s} \right]$ , which can be a function of (temperature_of_REV ), .

The equation is solved with respect to:

$\mathbf{p_c}$ (liquid_water_pressure )

The relative liquid permeability tensor is given by the layer classes. Currently the equation can be used with the following layer classes and its children:

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

Viscosity is a function of temperature. Therefore, it is suggested be solved this equation with the Thermal Transport Equation even though a constant temperature can also be provided.

The class currently implements the weak linearized form of the equation above. Therefore, cell_matrix returns the Jacobian of the equation and cell_residual contains the weak form of the equation using the solution at the previous Newton step.

Usage Details:

For users: An example of how the equation is setup in the input file is (assuming there is only one equation being solved in this case):

* subsection System management
* set Number of solution variables = 1
*     subsection Solution variables
*          set Solution variable 1 = liquid_pressure
*     end
* subsection Equations
*     set Equation 1 = Liquid Water Transport Equation
*     end
* end
* 

Boundary conditions

To be well-posed, these equations are equipped with the appropriate boundary conditions. All the boundary conditions can be described by boundary_id (p_c) and boundary_type.

Some boundary types require additional information, which can also be provided by the parameter file. We consider following types of boundary conditions:

No liquid water flux / Symmetric: A particular case of Neumann boundary condition.

Remarks

There is no provision to specify boundary indicators for No liquid water flux or Symmetric boundary conditions, as FEM formulation automatically implies a particular boundary is one of these cases, by default.

Usage Details:

For users:

* subsection Equations
*     subsection Liquid Water Transport Equation
*         set Liquid pressure at GDL Channel interface, [Pa]                 =  100.0
*         set Breakthrough liquid pressure at GDL Channel interface, [Pa]    =  0.0
*         set Breakthrough phenomenon at GDL/channel interface                  =  false
*     subsection Boundary data
*         set liquid_pressure = 4: -5e7
*     end
*     subsection Boundary conditions
*         set Constant liquid pressure current flux boundary conditions      =  2: 1e-3
*     end
* end
* 

Note that the breakthrough pressure is measured experimentally. If the breakthrough phenomenon has been turned off, a fixed pressure will be imposed on the GDL channel interface. The current flux of pressure on the boundary is the a parameter which controls how much liquid flux can go from the boundary.

Usage Details:

* // Creating Equation object (in Application Header file)
* FuelCellShop::Equation::LiquidPressureEquation<dim> liquid_transport;
* 
* // Declare parameters in application
* liquid_transport.declare_parameters(param);
* 
* // Initialize in application
* liquid_transport.initialize(param);
* 
* // Create a temporary vector in the application for storing couplings_map from all the equation used in the application.
* std::vector<couplings_map> tmp;
* ... // other equations
* tmp.push_back( liquid_transport.get_internal_cell_couplings() );
* 
* // Making cell couplings using SystemManagement object created in the application
* system_management.make_cell_couplings(tmp);
* 
* // cell_matrix in application
* // Do a check against layer and it should match with the layers currently working for this equation class.
* // for eg: CCL is FuelCellShop::Layer::HomogeneousCL<dim> object.
* liquid_transport.assemble_cell_matrix(cell_matrices, cell_info, &CCL);
* 
* // cell_residual in application
* liquid_transport.assemble_cell_residual(cell_vector, cell_info, &CCL); 
* 

Note: This class will work if thermal transport equation and fick's diffusion equation for water vapour is not solved for in the application. But it is always suggested to solve with those two equations together.This class does not assemble the phase change source/sink term for the water vapour transport inside the layers.

Author: J. Zhou, Marc Secanell 2015

Constructor & Destructor Documentation

template<int dim>

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

Constructor.

template<int dim>

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

virtual

Destructor.

Member Function Documentation

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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.

Currently, NOT IMPLEMENTED.

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

template<int dim>

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

virtual

Assemble local boundary residual.

Currently, NOT IMPLEMENTED.

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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::LiquidPressureEquation< dim >::assemble_cell_residual	(	FuelCell::ApplicationCore::FEVector &	cell_rhs,
		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::LiquidPressureEquation< dim >::declare_parameters ( ParameterHandler & param ) const

virtual

Declare parameters.

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

template<int dim>

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

virtual

Initialize parameters.

This class will call make_internal_cell_couplings and make_boundary_types.

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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 shape functions, normal_vectors, and JxW_bdry in Local CG FEM based assemblers - variable data (boundary) .

Currently, NOT IMPLEMENTED.

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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 (boundary) .

Currently, NOT IMPLEMENTED.

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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 shape functions, shape function gradients, and JxW_cell in Local CG FEM based assemblers - variable data (cell) .

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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 (cell) .

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< dim >::make_assemblers_generic_constant_data ( )

protectedvirtual

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

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< dim >::make_boundary_types ( )

inlineprotectedvirtual

This function fills out boundary_types.

Currently, NOT IMPLEMENTED.

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

template<int dim>

virtual void FuelCellShop::Equation::LiquidPressureEquation< 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::LiquidPressureEquation< dim >::make_output_types ( )

inlineprotectedvirtual

This function fills out output_types.

Currently, NOT IMPLEMENTED.

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

template<int dim>

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

virtual

The function prints out the equation's info.

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

Member Data Documentation

template<int dim>

bool FuelCellShop::Equation::LiquidPressureEquation< dim >::breakthrough_phenomenon

protected

This data member is set to true when the following boundary condition is to be applied at the boundary $N = k (p_{c(threshold)} - p_c)$ .

* subsection subsection Equations
*   subsection Liquid Water liquid Transport Equation
*   set Breakthrough phenomenon at GDL/channel interface           =  true
*   end
* end
* 

template<int dim>

std::map<unsigned int, double> FuelCellShop::Equation::LiquidPressureEquation< dim >::capillary_pressure_current_flux_map

protected

The map is used as the $ k_1 $ parameter in $N = k_1 (p_{c(threshold)} - p_c)$ .

* subsection subsection Equations
*   subsection Liquid Water liquid Transport Equation
*   set Constant liquid Pressure Current Flux Boundary Conditions =  2: 1e-3
*   end
* end
* 

template<int dim>

bool FuelCellShop::Equation::LiquidPressureEquation< dim >::cell_residual_counter

protected

Counter set to TRUE when cell_residual is being assembled.

This ensures that only effective transport properties are calculated, not their derivatives. (improves speed)

template<int dim>

std::vector< Tensor<2,dim> > FuelCellShop::Equation::LiquidPressureEquation< dim >::dT_rhok_mu_cell

protected

Computing the derivitive with respect to $ T $ in the function $\frac{\rho_l \hat{k}_l(p_c)}{\mu_l(T)}$ , at all quadrature points in the cell.

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::fickswater_blockindex_pliquid

protected

Block index for "liquid_pressure" corresponding to "Ficks Transport Equation - water".

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::fickswater_blockindex_trev

protected

Block index for "temperature_of_REV" corresponding to "Ficks Transport Equation - water".

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::fickswater_blockindex_xwater

protected

Block index for "water_molar_fraction" corresponding to "Ficks Transport Equation - water".

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::LiquidPressureEquation< dim >::grad_phi_p_cell

protected

$\mathbf{p_c}$ shape function gradients.

grad_phi_p_cell [ q ] [ k ] denotes $ k $ -th $\mathbf{p_c}$ shape function gradient computed in $ q $ -th quadrature point of the cell.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::LiquidPressureEquation< dim >::grad_phi_T_cell

protected

$\mathbf{T}$ shape function gradients.

grad_phi_T_cell [ q ] [ k ] denotes $ k $ -th $\mathbf{T}$ shape function gradient computed in $ q $ -th quadrature point of the cell.

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::k_sat

protected

Saturated permeability inside the porous media, $k_{sat} ~\left[ cm^2 \right]$ .

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::k_sat_bdry

protected

Saturated permeability at the boundary of the domain, $k_{satbdry} ~\left[ cm^2 \right]$ .

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::last_iter_bdry

protected

Variable used to store the index in bdry_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute bdry_matrix and bdry_residual.

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::last_iter_cell

protected

Variable used to store the index in cell_info->global_data of the previous Newton solution The solution at the previous iteration is used to compute cell_matrix and cell_residual.

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::M_water

protected

Molar weight of water in grams/mole.

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::p_cell

protected

Total pressure $\left[ Pa \right]$ in the cell.

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::p_channel_GDL

protected

The boundary condition term which indicates the liquid pressure (Pa) $p_{c(threshold1)}$ in $N = k_1 (p_{c(threshold1)} - p_c)$ .

* subsection subsection Equations
*   subsection Liquid Water liquid Transport Equation
*   set liquid pressure at GDL Channel interface, [Pa]                 =  100.0
*   end
* end
* 

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::p_channel_GDL_second

protected

The boundary condition term which indicates the breakthrough liquid pressure (Pa).

This is initialized

* subsection subsection Equations
*   subsection Liquid Water liquid Transport Equation
*   set Breakthrough liquid pressure at GDL Channel interface, [Pa]          =  0.0
*   end
* end
* 

template<int dim>

VariableInfo FuelCellShop::Equation::LiquidPressureEquation< dim >::p_liquid_water

protected

VariableInfo structure corresponding to "liquid_pressure".

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::LiquidPressureEquation< dim >::phi_p_cell

protected

$\mathbf{p_c}$ shape functions.

phi_p_cell [ q ] [ k ] denotes $ k $ -th $\mathbf{p_c}$ shape function computed in $ q $ -th quadrature point of the cell.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::LiquidPressureEquation< dim >::phi_p_cell_bdry

protected

$\mathbf{p_c}$ shape functions at the boundary.

phi_p_cell_bdry [ q ] [ k ] denotes $ k $ -th $\mathbf{p_c}$ shape function computed in $ q $ -th quadrature point at the boundary.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::LiquidPressureEquation< dim >::phi_T_cell

protected

$\mathbf{T}$ shape functions.

phi_T_cell [ q ] [ k ] denotes $ k $ -th $\mathbf{T}$ shape function computed in $ q $ -th quadrature point of the cell.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::LiquidPressureEquation< dim >::phi_xwater_cell

protected

$\mathbf{x_{H_2O}}$ shape functions.

phi_xwater_cell [ q ] [ k ] denotes $ k $ -th $\mathbf{x_{H_2O}}$ shape function computed in $ q $ -th quadrature point of the cell.

template<int dim>

std::vector<bool> FuelCellShop::Equation::LiquidPressureEquation< dim >::reached_breakthrough_pressure

protected

Once the liquid pressure at the GDL and channel interface reaches the breakthrouhg pressure the following boundary condition is to set to be applied $N = k (p_{c(threshold)} - p_c)$ .

And this vector of bool is set to be true to lock the boundary condition.

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::rho_l

protected

Density of liquid water, $\rho_l ~\left[ \frac{g}{cm^3} \right]$ .

template<int dim>

std::vector< Tensor<2,dim> > FuelCellShop::Equation::LiquidPressureEquation< dim >::rho_mu_dk_dp_cell

protected

Computing the derivitive with respect to $ p_c $ in the function $\frac{\rho_l \hat{k}_l(p_c)}{\mu_l(T)}$ , at all quadrature points in the cell.

template<int dim>

std::vector< Tensor<2,dim> > FuelCellShop::Equation::LiquidPressureEquation< dim >::rhok_mu_cell

protected

$\frac{\rho_l \hat{k}_l}{\mu_l}$ , at all quadrature points in the cell.

template<int dim>

std::vector< Tensor<2,dim> > FuelCellShop::Equation::LiquidPressureEquation< dim >::rhok_mu_cell_bdry

protected

$\frac{\rho_l \hat{k}_l}{\mu_l}$ , at all quadrature points in the boundary.

template<int dim>

VariableInfo FuelCellShop::Equation::LiquidPressureEquation< dim >::t_rev

protected

VariableInfo structure corresponding to "temperature_of_REV".

template<int dim>

double FuelCellShop::Equation::LiquidPressureEquation< dim >::temperature

protected

Temperature [in K] of the layer.

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::thermal_blockindex_pliquid

protected

Block index for "liquid_pressure" corresponding to "Thermal Transport Equation".

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::thermal_blockindex_trev

protected

Block index for "temperature_of_REV" corresponding to "Thermal Transport Equation".

template<int dim>

unsigned int FuelCellShop::Equation::LiquidPressureEquation< dim >::thermal_blockindex_xwater

protected

Block index for "water_molar_fraction" corresponding to "Thermal Transport Equation".

template<int dim>

VariableInfo FuelCellShop::Equation::LiquidPressureEquation< dim >::x_water

protected

VariableInfo structure corresponding to "water_molar_fraction".

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

liquid_transport_equation.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

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

Governing equation

Usage Details:

Boundary conditions

Usage Details:

Usage Details:

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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