This class deals with Membrane Water Content Transport Equation. More...

#include <lambda_transport_equation.h>

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

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

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

virtual	~LambdaTransportEquation ()
	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...

Boolean flags for lambda transport modes
bool	flag_thermoosmosis
	Flag to indicate that lambda (sorbed water) transport by Thermo-osmosis is ON or OFF. More...

Generic Constant Data
VariableInfo	phi_m
	VariableInfo structure corresponding to `"protonic_electrical_potential"`. More...

VariableInfo	lambda
	VariableInfo structure corresponding to `"membrane_water_content"`. More...

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

double	F
	Universal Faraday's constant. More...

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

Local CG FEM based assemblers - variable data (cell)
double	rho_dry_cell
	Density [`gm/cm^3`] of the dry polymer electrolyte material in the cell. More...

double	EW_cell
	Equivalent weight of the polymer electrolyte material in the cell. More...

std::vector< double >	nDrag_cell
	Electro-osmotic drag coefficient, at all quadrature points in the cell. More...

std::vector< double >	dnDrag_dlambda_cell
	Derivative of electro-osmotic drag coefficient w.r.t. More...

std::vector< double >	sigmaMeff_cell
	Effective proton conductivity [`S/cm`], at all quadrature points of the cell. More...

std::vector< double >	dsigmaMeff_dT_cell
	Derivative of effective protonic conductivity w.r.t `"temperature_of_REV"`, at all quadrature points in the cell. More...

std::vector< double >	dsigmaMeff_dlambda_cell
	Derivative of effective protonic conductivity w.r.t. More...

std::vector< double >	Dlambdaeff_cell
	Effecive lambda (sorbed water) diffusivity [`cm^2/s`], at all quadrature points in the cell. More...

std::vector< double >	dDlambdaeff_dT_cell
	Derivative of effective lambda diffusivity w.r.t. More...

std::vector< double >	dDlambdaeff_dlambda_cell
	Derivative of effective lambda diffusivity w.r.t. More...

std::vector< double >	DTeff_cell
	Effecive thermo-osmotic diffusion coefficient [`gm/(cm-s-K`)], at all quadrature points in the cell. More...

std::vector< double >	dDTeff_dT_cell
	Derivative of effective thermo-osmotic diffusion coefficient w.r.t. More...

std::vector< std::vector < double > >	phi_lambda_cell
	$\mathbf{\lambda}$ shape functions. More...

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

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

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

std::vector< std::vector < Tensor< 1, dim > > >	grad_phi_phiM_cell
	$\mathbf{\phi_m}$ 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::LambdaTransportEquation< dim >

This class deals with Membrane Water Content Transport Equation.

This equation class solves for water transport inside the membrane using semi-empirical model proposed by Springer et al. According to Springer model, sorbed water $( \lambda )$ inside the membrane is transported via electro-osmotic drag and fickian diffusion. Besides this, under nonisothermal conditions, water flows from cold to hot side causing thermal osmosis. These three transport modes are currently being considered in this equation class.

It is to be noted that this model is suitable for water-vapor equilibriated membranes or isobaric membranes. Under such conditions, convective transport can be neglected.

It is solved with respect to:

$\mathbf{\lambda}$ (membrane_water_content )

where, $\lambda = \frac{moles~of~sorbed~water}{moles~of~SO_3^-}$ .

This equation can be written as:

$\qquad \mathbf{\nabla} \cdot \left( \frac{n_d}{F} \hat{\sigma}_{m,eff} \mathbf{\nabla} \phi_m + \frac{\rho_{dry}}{EW} \hat{D}_{\lambda,eff} \mathbf{\nabla} \lambda + \frac{1}{M_{water}} \hat{D}_{T,eff} \mathbf{\nabla} T \right) = 0 \quad \in \quad \Omega$

where, first term corresponds to electro-osmotic drag, second term corresponds to fickian diffusion and third term corresponds to thermo-osmotic diffusion.
$\hat{\sigma}_{m,eff}$ is effective proton conductivity tensor [S/cm], which can be function of other variables, viz., $\lambda$ (membrane_water_content ) and (temperature_of_REV ).
$\hat{D}_{\lambda,eff}$ is effective lambda (sorbed water) diffusivity tensor [cm^2/s], which can be function of other variables, viz., $\lambda$ (membrane_water_content ) and (temperature_of_REV ).
$\hat{D}_{T,eff}$ is effective thermo-osmotic diffusivity tensor [gm/(cm-s-K )], which can be a function of (temperature_of_REV ).
is electro-osmotic drag coefficient.
is Faraday's constant.
$\rho_{dry}$ is dry polymer electrolyte material density [gm/cm^3].
$EW = \frac{mass~of~dry~polymer~electrolyte~material~in~grams}{moles~of~SO_3^-}$ is equivalent weight.
$M_{water}$ is molar weight of water [gm/moles]
$\mathbf{\phi_{m}}$ (protonic_electrical_potential )

To be well-posed, these equations are equipped with the appropriate boundary conditions. All the boundary conditions can be described by boundary_id (s ) and boundary_type. Besides, this some boundary types require additional information, which can also be provided by the parameter file. We consider following types of boundary conditions:

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

Remarks

There is no provision to specify boundary indicators for No water flux or Symmetric boundary conditions, as FEM formulation automatically implies a particular boundary is one of these cases, by default.
This class works with the following layer classes only:
- FuelCellShop::Layer::CatalystLayer<dim>
- FuelCellShop::Layer::MembraneLayer<dim>
Thermo-osmotic diffusion is set to OFF by default, but can be turned ON based on the flag set in the parameter file.
There is no direct flag for setting electro-osmotic drag ON or OFF, it is defaulted to ON, if $\phi_m$ is also one of the solution variables. But even in this case, it can be indirectly set to OFF by setting , electro-osmotic drag coefficient to 0 in the parameter file for Nafion material class.

We solve the whole problem by linearizing the governing equation at each Newton iteration with subsequent CG FEM discretization in space. The class contains the necessary class members to add the necessary contributions to cell_matrix and cell_residual to the governing equations used to analyze lambda transport,

Usage Details:

* // Creating Equation object (in Application Header file)
* FuelCellShop::Equation::LambdaTransportEquation<dim> lambda_transport;
*
* // Declare parameters in application
* lambda_transport.declare_parameters(param);
*
* // Initialize in application
* lambda_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( lambda_transport.get_internal_cell_couplings() );
*
* // Look at SorptionSourceTerms class here, if source terms due to water sorption/desorption are to be considered.
* // 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.
* lambda_transport.assemble_cell_matrix(cell_matrices, cell_info, &CCL);
*
* // cell_residual in application
* lambda_transport.assemble_cell_residual(cell_vector, cell_info, &CCL);
* 

Note: This class doesn't assemble for water sorption/desorption source terms; that is taken care off by SorptionSourceTerms class. Please read the documentation of SorptionSourceTerms class, for additional methods to be implemented in the application.

Warning: If water sorption/desorption source terms are being considered, it's very important to use adjust_internal_cell_couplings member function of SorptionSourceTerms class, before using make_cell_couplings of SystemManagement at the application level.

Author: Madhur Bhaiya, 2013; Valentin N. Zingan, 2012-2014 - afterward improvements, optimization, checkings, CG FEM bug fixings

Constructor & Destructor Documentation

template<int dim>

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

Constructor.

template<int dim>

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

virtual

Destructor.

Member Function Documentation

template<int dim>

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

inlinevirtual

Assemble local boundary matrix.

Currently, NOT IMPLEMENTED.

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

template<int dim>

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

inlinevirtual

Assemble local boundary residual.

Currently, NOT IMPLEMENTED.

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

template<int dim>

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

virtual

Declare parameters.

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

template<int dim>

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

inlineprotectedvirtual

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

inlineprotectedvirtual

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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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::LambdaTransportEquation< 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<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dDlambdaeff_dlambda_cell

protected

Derivative of effective lambda diffusivity w.r.t.

"membrane_water_content", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dDlambdaeff_dT_cell

protected

Derivative of effective lambda diffusivity w.r.t.

"temperature_of_REV", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dDTeff_dT_cell

protected

Derivative of effective thermo-osmotic diffusion coefficient w.r.t.

"temperature_of_REV", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::Dlambdaeff_cell

protected

Effecive lambda (sorbed water) diffusivity [cm^2/s], at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dnDrag_dlambda_cell

protected

Derivative of electro-osmotic drag coefficient w.r.t.

"membrane_water_content", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dsigmaMeff_dlambda_cell

protected

Derivative of effective protonic conductivity w.r.t.

"membrane_water_content", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::dsigmaMeff_dT_cell

protected

Derivative of effective protonic conductivity w.r.t "temperature_of_REV", at all quadrature points in the cell.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::DTeff_cell

protected

Effecive thermo-osmotic diffusion coefficient [gm/(cm-s-K)], at all quadrature points in the cell.

template<int dim>

double FuelCellShop::Equation::LambdaTransportEquation< dim >::EW_cell

protected

Equivalent weight of the polymer electrolyte material in the cell.

template<int dim>

double FuelCellShop::Equation::LambdaTransportEquation< dim >::F

protected

Universal Faraday's constant.

template<int dim>

bool FuelCellShop::Equation::LambdaTransportEquation< dim >::flag_thermoosmosis

protected

Flag to indicate that lambda (sorbed water) transport by Thermo-osmosis is ON or OFF.

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::LambdaTransportEquation< dim >::grad_phi_lambda_cell

protected

$\mathbf{\lambda}$ shape function gradients.

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

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::LambdaTransportEquation< dim >::grad_phi_phiM_cell

protected

$\mathbf{\phi_m}$ shape function gradients.

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

template<int dim>

std::vector< std::vector< Tensor<1,dim> > > FuelCellShop::Equation::LambdaTransportEquation< 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>

VariableInfo FuelCellShop::Equation::LambdaTransportEquation< dim >::lambda

protected

VariableInfo structure corresponding to "membrane_water_content".

template<int dim>

unsigned int FuelCellShop::Equation::LambdaTransportEquation< 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::LambdaTransportEquation< dim >::M_water

protected

Molar weight of water in grams/mole.

template<int dim>

std::vector<double> FuelCellShop::Equation::LambdaTransportEquation< dim >::nDrag_cell

protected

Electro-osmotic drag coefficient, at all quadrature points in the cell.

template<int dim>

std::vector< std::vector<double> > FuelCellShop::Equation::LambdaTransportEquation< dim >::phi_lambda_cell

protected

$\mathbf{\lambda}$ shape functions.