Transport with dispersion implemented using discontinuous Galerkin method. More...

#include <transport_dg.hh>

Inheritance diagram for TransportDG< Model >:

Collaboration diagram for TransportDG< Model >:

Classes
class	EqData

Public Types
enum	DGVariant { non_symmetric = -1, incomplete = 0, symmetric = 1 }

Public Types inherited from EquationForMassBalance
enum	TimeIntegrationScheme { none, explicit_euler, implicit_euler, crank_nicholson }

Public Member Functions
	TransportDG (Mesh &init_mesh, const Input::Record &in_rec)
	Constructor. More...

void	zero_time_step () override
	Initialize solution in the zero time. More...

void	update_solution () override
	Computes the solution in one time instant. More...

virtual void	set_velocity_field (const MH_DofHandler &dh)
	Updates the velocity field which determines some coefficients of the transport equation. More...

void	output_data ()
	Postprocesses the solution and writes to output file. More...

virtual EqData *	get_data ()
	Getter for field data. More...

TimeIntegrationScheme	time_scheme ()
	Returns the time integration scheme of the equation. More...

	~TransportDG ()
	Destructor. More...

template<unsigned int dim>
void	calculate_velocity (const typename DOFHandlerBase::CellIterator &cell, vector< arma::vec3 > &velocity, FEValuesBase< dim, 3 > &fv)

Public Member Functions inherited from TransportBase
	TransportBase (Mesh &mesh, const Input::Record in_rec)

virtual	~TransportBase ()

MassBalance *	mass_balance ()

unsigned int	n_substances () override
	Returns number of trnasported substances. More...

vector< string > &	substance_names () override
	Returns reference to the vector of substnace names. More...

virtual void	set_concentration_vector (Vec &vec)

Public Member Functions inherited from AdvectionProcessBase
	AdvectionProcessBase (Mesh &mesh, const Input::Record in_rec)

Public Member Functions inherited from EquationBase
	EquationBase ()

	EquationBase (Mesh &mesh, const Input::Record in_rec)

virtual	~EquationBase ()

virtual void	initialize ()
	Initialize fields. More...

virtual void	choose_next_time ()

virtual void	set_time_upper_constraint (double dt)

virtual void	set_time_lower_constraint (double dt)

TimeGovernor const &	time ()

virtual void	set_time_governor (TimeGovernor &time)

double	planned_time ()

double	solved_time ()

Mesh &	mesh ()

TimeMark::Type	mark_type ()

FieldSet &	data ()

virtual void	get_solution_vector (double *&vector, unsigned int &size)

virtual void	get_parallel_solution_vector (Vec &vector)

Public Member Functions inherited from EquationForMassBalance
virtual	~EquationForMassBalance ()

Static Public Attributes
static Input::Type::Record	input_type
	Declare input record type for the equation TransportDG. More...

static Input::Type::Selection	dg_variant_selection_input_type
	Input type for the DG variant selection. More...

Static Public Attributes inherited from TransportBase
static Input::Type::Record	input_type_output_record

Static Public Attributes inherited from AdvectionProcessBase
static Input::Type::AbstractRecord	input_type
	Common specification of the input record for secondary equations. More...

Private Member Functions
Model::ModelEqData &	data ()

void	output_vector_gather ()

void	assemble_mass_matrix ()
	Assembles the mass matrix. More...

template<unsigned int dim>
void	assemble_mass_matrix ()
	Assembles the mass matrix for the given dimension. More...

void	assemble_stiffness_matrix ()
	Assembles the stiffness matrix. More...

template<unsigned int dim>
void	assemble_volume_integrals ()
	Assembles the volume integrals into the stiffness matrix. More...

void	set_sources ()
	Assembles the right hand side due to volume sources. More...

template<unsigned int dim>
void	set_sources ()
	Assembles the right hand side vector due to volume sources. More...

template<unsigned int dim>
void	assemble_fluxes_boundary ()
	Assembles the fluxes on the boundary. More...

template<unsigned int dim>
void	assemble_fluxes_element_element ()
	Assembles the fluxes between elements of the same dimension. More...

template<unsigned int dim>
void	assemble_fluxes_element_side ()
	Assembles the fluxes between elements of different dimensions. More...

void	set_boundary_conditions ()
	Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions. More...

template<unsigned int dim>
void	set_boundary_conditions ()
	Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions for a given space dimension. More...

template<unsigned int dim>
void	calculate_velocity (const ElementFullIter &cell, std::vector< arma::vec3 > &velocity, FEValuesBase< dim, 3 > &fv)
	Calculates the velocity field on a given `dim` dimensional cell. More...

void	calculate_dispersivity_tensor (arma::mat33 &K, const arma::vec3 &velocity, double Dm, double alphaL, double alphaT, double porosity, double cross_cut)
	Calculates the dispersivity (diffusivity) tensor from the velocity field. More...

void	set_DG_parameters_edge (const Edge &edg, const int s1, const int s2, const int K_size, const std::vector< arma::mat33 > &K1, const std::vector< arma::mat33 > &K2, const std::vector< double > &fluxes, const arma::vec3 &normal_vector, const double alpha1, const double alpha2, double &gamma, double *omega, double &transport_flux)
	Sets up some parameters of the DG method for two sides of an edge. More...

void	set_DG_parameters_boundary (const SideIter side, const int K_size, const std::vector< arma::mat33 > &K, const double flux, const arma::vec3 &normal_vector, const double alpha, double &gamma)
	Sets up parameters of the DG method on a given boundary edge. More...

void	set_initial_condition ()
	Sets the initial condition. More...

template<unsigned int dim>
void	prepare_initial_condition ()
	Assembles the auxiliary linear system to calculate the initial solution as L^2-projection of the prescribed initial condition. More...

void	calc_fluxes (vector< vector< double > > &bcd_balance, vector< vector< double > > &bcd_plus_balance, vector< vector< double > > &bcd_minus_balance)
	Calculates flux through boundary of each region. More...

template<unsigned int dim>
void	calc_fluxes (vector< vector< double > > &bcd_balance, vector< vector< double > > &bcd_plus_balance, vector< vector< double > > &bcd_minus_balance)
	Calculates flux through boundary of each region of specific dimension. More...

void	calc_elem_sources (vector< vector< double > > &mass, vector< vector< double > > &src_balance)
	Calculates volume sources for each region. More...

template<unsigned int dim>
void	calc_elem_sources (vector< vector< double > > &mass, vector< vector< double > > &src_balance)
	Calculates volume sources for each region of specific dimension. More...

Private Attributes
Physical parameters
EqData	data_
	Field data for model parameters. More...

Parameters of the numerical method
FEObjects *	feo
	Finite element objects. More...

std::vector< std::vector < double > >	gamma
	Penalty parameters. More...

int	dg_variant
	DG variant ((non-)symmetric/incomplete. More...

unsigned int	dg_order
	Polynomial order of finite elements. More...

Solution of algebraic system
Vec *	rhs
	Vector of right hand side. More...

Mat *	stiffness_matrix
	The stiffness matrix. More...

Mat	mass_matrix
	The mass matrix. More...

LinSys **	ls
	Linear algebra system for the transport equation. More...

LinSys *	ls_dt
	Linear algebra system for the time derivative (actually it is used only for handling the matrix structures). More...

Output to file
vector< double * >	output_solution
	Array for storing the output solution data. More...

vector< Vec >	output_vec
	Vector of solution data. More...

Input::Record	output_rec
	Record with output specification. More...

OutputTime *	output_stream

Auxiliary fields used during assembly
vector< double >	mm_coef
	Mass matrix coefficients. More...

vector< vector< arma::vec3 > >	ad_coef
	Advection coefficients. More...

vector< vector< arma::mat33 > >	dif_coef
	Diffusion coefficients. More...

vector< vector< vector < arma::vec3 > > >	ad_coef_edg
	Advection coefficients on edges. More...

vector< vector< vector < arma::mat33 > > >	dif_coef_edg
	Diffusion coefficients on edges. More...

Other
bool	allocation_done
	Indicates whether matrices have been preallocated. More...

Additional Inherited Members
Protected Member Functions inherited from TransportBase
const RegionDB *	region_db ()
	Returns the region database. More...

Protected Attributes inherited from TransportBase
unsigned int	n_subst_
	Number of transported substances. More...

std::vector< string >	subst_names_
	Names of transported substances. More...

const MH_DofHandler *	mh_dh

MassBalance *	mass_balance_
	object for calculation and writing the mass balance to file. More...

Protected Attributes inherited from EquationBase
bool	equation_empty_
	flag is true if only default constructor was called More...

Mesh *	mesh_

TimeGovernor *	time_

Input::Record	input_record_

FieldSet *	eq_data_

Detailed Description

template<class Model>
class TransportDG< Model >

Transport with dispersion implemented using discontinuous Galerkin method.

TransportDG implements the discontinuous Galerkin method for the transport and diffusion of substances. The concentration $ c_i ~[kg/m^3]$ of the i-th substance is governed by the advection-diffusion equation

$\partial_t c_i + \mathbf v\cdot\nabla c_i - \mathrm{div}(D\nabla c_i) = F \mbox{ in }\Omega^d,$

where $\mathbf v$ is the fluid velocity and $\Omega^d$ the $d$ -dimensional domain, respectively. The hydrodynamic dispersivity tensor $\mathbf D ~[m^2/s]$ is given by:

$\mathbf D = D_m\mathbf I + |\mathbf v|\left(\alpha_T\mathbf I + (\alpha_L-\alpha_T)\frac{\mathbf v\otimes\mathbf v}{|\mathbf v|^2}\right).$

The molecular dispersivity $D_m~[m^2/s]$ , as well as the longitudal and transversal dispersivity $\alpha_L,~\alpha_T~[m]$ are input parameters of the model.

For lower dimensions $d=1,2$ the advection-diffusion equation is multiplied by the fracture cross-cut $\delta^d~[m^{3-d}]$ .

The boundary $\partial\Omega^d$ is divided into three disjoint parts $\Gamma^d_D\cup\Gamma^d_N\cup\Gamma^d_F$ . We prescribe the following boundary conditions:

$\begin{eqnarray*} c_i^d &= c_{iD}^d &\mbox{ on }\Gamma^d_D \mbox{ (Dirichlet)},\\ \mathbf D^d\nabla c_i^d\cdot\mathbf n &= 0 &\mbox{ on }\Gamma^d_N \mbox{ (Neumann)}, \end{eqnarray*}$

The transfer of mass through fractures is described by the transmission conditions on $\Gamma^d_F$ :

$-\mathbf D^d\nabla c_i^d\cdot\mathbf n = \sigma(c_i^d-c_i^{d-1}) + \left\{\begin{array}{cl}0 &\mbox{ if }\mathbf v^d\cdot\mathbf n\ge 0\\\mathbf v^d\cdot\mathbf n(c_i^{d-1}-c_i^d) & \mbox{ if }\mathbf v^d\cdot\mathbf n<0\end{array}\right.,\qquad F^{d-1} = (\sigma + |\mathbf v^d\cdot\mathbf n|)(c_i^d-c_i^{d-1}).$

Here $\mathbf n$ stands for the unit outward normal vector to $\partial\Omega^d$ . The coefficient $\sigma$ determines the transfer of mass through fractures due to diffusion.

Definition at line 137 of file transport_dg.hh.

Member Enumeration Documentation

template<class Model>

enum TransportDG::DGVariant

Enumerator
non_symmetric
incomplete
symmetric

Definition at line 167 of file transport_dg.hh.

Constructor & Destructor Documentation

template<class Model >

TransportDG< Model >::TransportDG	(	Mesh &	init_mesh,
		const Input::Record &	in_rec
	)

Constructor.

Parameters

init_mesh	computational mesh
in_rec	input record

Definition at line 233 of file transport_dg.cc.

template<class Model >

TransportDG< Model >::~TransportDG ( )

Destructor.

Definition at line 341 of file transport_dg.cc.

Member Function Documentation

template<class Model >

template<unsigned int dim>

void TransportDG< Model >::assemble_fluxes_boundary ( )

private

Assembles the fluxes on the boundary.

Definition at line 901 of file transport_dg.cc.

template<class Model >

template<unsigned int dim>

void TransportDG< Model >::assemble_fluxes_element_element ( )

private

Assembles the fluxes between elements of the same dimension.

Definition at line 770 of file transport_dg.cc.

template<class Model >

template<unsigned int dim>

void TransportDG< Model >::assemble_fluxes_element_side ( )

private

Assembles the fluxes between elements of different dimensions.

Definition at line 990 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::assemble_mass_matrix ( )

private

Assembles the mass matrix.

The routine just calls templated method assemble_mass_matrix() for each space dimension.

Definition at line 577 of file transport_dg.cc.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::assemble_mass_matrix ( )

private

Assembles the mass matrix for the given dimension.

template<class Model >

void TransportDG< Model >::assemble_stiffness_matrix ( )

private

Assembles the stiffness matrix.

This routine just calls assemble_volume_integrals(), assemble_fluxes_boundary(), assemble_fluxes_element_element() and assemble_fluxes_element_side() for each space dimension.

Definition at line 626 of file transport_dg.cc.

template<class Model >

template<unsigned int dim>

void TransportDG< Model >::assemble_volume_integrals ( )

private

Assembles the volume integrals into the stiffness matrix.

Definition at line 659 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::calc_elem_sources	(	vector< vector< double > > &	mass,
		vector< vector< double > > &	src_balance
	)

privatevirtual

Calculates volume sources for each region.

This method actually calls calc_elem_sources<dim>() for each space dimension.

Parameters

mass	Vector of substance mass per region.
src_balance	Vector of sources per region.

Implements EquationForMassBalance.

Definition at line 1523 of file transport_dg.cc.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::calc_elem_sources	(	vector< vector< double > > &	mass,
		vector< vector< double > > &	src_balance
	)

privatevirtual

Calculates volume sources for each region of specific dimension.

Parameters

mass	Vector of substance mass per region.
src_balance	Vector of sources per region.

Implements EquationForMassBalance.

template<class Model >

void TransportDG< Model >::calc_fluxes	(	vector< vector< double > > &	bcd_balance,
		vector< vector< double > > &	bcd_plus_balance,
		vector< vector< double > > &	bcd_minus_balance
	)

privatevirtual

Calculates flux through boundary of each region.

This actually calls calc_fluxes<dim>() for each space dimension.

Parameters

bcd_balance	Total fluxes.
bcd_plus_balance	Incoming fluxes.
bcd_minus_balance	Outgoing fluxes.

Implements EquationForMassBalance.

Definition at line 1436 of file transport_dg.cc.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::calc_fluxes	(	vector< vector< double > > &	bcd_balance,
		vector< vector< double > > &	bcd_plus_balance,
		vector< vector< double > > &	bcd_minus_balance
	)

privatevirtual

Calculates flux through boundary of each region of specific dimension.

Parameters

bcd_balance	Total fluxes.
bcd_plus_balance	Incoming fluxes.
bcd_minus_balance	Outgoing fluxes.

Implements EquationForMassBalance.

template<class Model>

void TransportDG< Model >::calculate_dispersivity_tensor	(	arma::mat33 &	K,
		const arma::vec3 &	velocity,
		double	Dm,
		double	alphaL,
		double	alphaT,
		double	porosity,
		double	cross_cut
	)

private

Calculates the dispersivity (diffusivity) tensor from the velocity field.

Parameters

K	The computed dispersivity tensor.
velocity	The velocity field (at quadrature points).
Dm	Molecular diffusivities.
alphaL	Longitudal dispersivities.
alphaT	Transversal dispersivities.
porosity	Porosities.
cross_cut	Cross-cuts of higher dimension.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::calculate_velocity	(	const ElementFullIter &	cell,
		std::vector< arma::vec3 > &	velocity,
		FEValuesBase< dim, 3 > &	fv
	)

private

Calculates the velocity field on a given dim dimensional cell.

Parameters

cell	The cell.
velocity	The computed velocity field (at quadrature points).
fv	The FEValues class providing the quadrature points and the shape functions for velocity.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::calculate_velocity	(	const typename DOFHandlerBase::CellIterator &	cell,
		vector< arma::vec3 > &	velocity,
		FEValuesBase< dim, 3 > &	fv
	)

Definition at line 1196 of file transport_dg.cc.

template<class Model>

Model::ModelEqData& TransportDG< Model >::data ( )

inlineprivate

Definition at line 234 of file transport_dg.hh.

template<class Model>

virtual EqData* TransportDG< Model >::get_data ( )

inlinevirtual

Getter for field data.

Definition at line 223 of file transport_dg.hh.

template<class Model >

void TransportDG< Model >::output_data ( void )

virtual

Postprocesses the solution and writes to output file.

Reimplemented from EquationBase.

Definition at line 557 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::output_vector_gather ( void )

private

Definition at line 374 of file transport_dg.cc.

template<class Model >

template<unsigned int dim>

void TransportDG< Model >::prepare_initial_condition ( )

private

Assembles the auxiliary linear system to calculate the initial solution as L^2-projection of the prescribed initial condition.

Definition at line 1385 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::set_boundary_conditions ( )

private

Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions.

The routine just calls templated method set_boundary_condition() for each space dimension.

Definition at line 1104 of file transport_dg.cc.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::set_boundary_conditions ( )

private

Assembles the r.h.s. components corresponding to the Dirichlet boundary conditions for a given space dimension.

template<class Model >

void TransportDG< Model >::set_DG_parameters_boundary	(	const SideIter	side,
		const int	K_size,
		const std::vector< arma::mat33 > &	K,
		const double	flux,
		const arma::vec3 &	normal_vector,
		const double	alpha,
		double &	gamma
	)

private

Sets up parameters of the DG method on a given boundary edge.

Assumption is that the edge consists of only 1 side.

Parameters

side	The boundary side.
K_size	Size of vector of tensors K.
K	Dispersivity tensor.
ad_vector	Advection vector.
normal_vector	Normal vector (assumed constant along the edge).
alpha	Penalty parameter that influences the continuity of the solution (large value=more continuity).
gamma	Computed penalty parameters.

Definition at line 1325 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::set_DG_parameters_edge	(	const Edge &	edg,
		const int	s1,
		const int	s2,
		const int	K_size,
		const std::vector< arma::mat33 > &	K1,
		const std::vector< arma::mat33 > &	K2,
		const std::vector< double > &	fluxes,
		const arma::vec3 &	normal_vector,
		const double	alpha1,
		const double	alpha2,
		double &	gamma,
		double *	omega,
		double &	transport_flux
	)

private

Sets up some parameters of the DG method for two sides of an edge.

Parameters

edg	The edge.
s1	Side 1.
s2	Side 2.
K_size	Size of vector of tensors K.
K1	Dispersivity tensors on side s1 (in quadrature points).
K2	Dispersivity tensors on side s2 (in quadrature points).
normal_vector	Normal vector to side 0 of the neighbour (assumed constant along the side).
alpha1,alpha2	Penalty parameter that influences the continuity of the solution (large value=more continuity).
gamma	Computed penalty parameters.
omega	Computed weights.
transport_flux	Computed flux from side s1 to side s2.

Definition at line 1223 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::set_initial_condition ( )

private

Sets the initial condition.

Definition at line 1360 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::set_sources ( )

private

Assembles the right hand side due to volume sources.

This method just calls set_sources() for each space dimension.

Definition at line 713 of file transport_dg.cc.

template<class Model>

template<unsigned int dim>

void TransportDG< Model >::set_sources ( )

private

Assembles the right hand side vector due to volume sources.

template<class Model >

void TransportDG< Model >::set_velocity_field ( const MH_DofHandler & dh )

virtual

Updates the velocity field which determines some coefficients of the transport equation.

Parameters

dh	mixed hybrid dof handler

(So far it does not work since the flow module returns a vector of zeros.)

Parameters

velocity_vector Input array of velocity values.

Reimplemented from TransportBase.

Definition at line 545 of file transport_dg.cc.

template<class Model>

TimeIntegrationScheme TransportDG< Model >::time_scheme ( )

inlinevirtual

Returns the time integration scheme of the equation.

Implements EquationForMassBalance.

Definition at line 225 of file transport_dg.hh.

template<class Model >

void TransportDG< Model >::update_solution ( void )

overridevirtual

Computes the solution in one time instant.

Reimplemented from EquationBase.

Definition at line 408 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::zero_time_step ( )

overridevirtual

Initialize solution in the zero time.

Reimplemented from EquationBase.

Definition at line 394 of file transport_dg.cc.

Member Data Documentation

template<class Model>

vector<vector<arma::vec3> > TransportDG< Model >::ad_coef

private

Advection coefficients.

Definition at line 515 of file transport_dg.hh.

template<class Model>

vector<vector<vector<arma::vec3> > > TransportDG< Model >::ad_coef_edg

private

Advection coefficients on edges.

Definition at line 519 of file transport_dg.hh.

template<class Model>

bool TransportDG< Model >::allocation_done

private

Indicates whether matrices have been preallocated.

Definition at line 532 of file transport_dg.hh.

template<class Model>

EqData TransportDG< Model >::data_

private

Field data for model parameters.

Definition at line 446 of file transport_dg.hh.

template<class Model>

unsigned int TransportDG< Model >::dg_order

private

Polynomial order of finite elements.

Definition at line 464 of file transport_dg.hh.

template<class Model>

int TransportDG< Model >::dg_variant

private

DG variant ((non-)symmetric/incomplete.

Definition at line 461 of file transport_dg.hh.

template<class Model>

Selection TransportDG< Model >::dg_variant_selection_input_type

static

Initial value:

= Selection("DG_variant", "Type of penalty term.")
    .add_value(non_symmetric, "non-symmetric", "non-symmetric weighted interior penalty DG method")
    .add_value(incomplete,    "incomplete",    "incomplete weighted interior penalty DG method")
    .add_value(symmetric,     "symmetric",     "symmetric weighted interior penalty DG method")

Input type for the DG variant selection.

Definition at line 193 of file transport_dg.hh.

template<class Model>

vector<vector<arma::mat33> > TransportDG< Model >::dif_coef

private

Diffusion coefficients.

Definition at line 517 of file transport_dg.hh.

template<class Model>

vector<vector<vector<arma::mat33> > > TransportDG< Model >::dif_coef_edg

private

Diffusion coefficients on edges.

Definition at line 521 of file transport_dg.hh.

template<class Model>

FEObjects* TransportDG< Model >::feo

private

Finite element objects.

Definition at line 455 of file transport_dg.hh.

template<class Model>

std::vector<std::vector<double> > TransportDG< Model >::gamma

private

Penalty parameters.

Definition at line 458 of file transport_dg.hh.

template<class Model>

Record TransportDG< Model >::input_type

static

Initial value:

= Model::get_input_type("DG", "DG solver")
    .declare_key("solver", LinSys_PETSC::input_type, Default::obligatory(),
            "Linear solver for MH problem.")
    .declare_key("input_fields", Array(TransportDG<Model>::EqData().make_field_descriptor_type(Model::ModelEqData::name() + "_DG")), IT::Default::obligatory(), "")
    .declare_key("dg_variant", TransportDG<Model>::dg_variant_selection_input_type, Default("non-symmetric"),
            "Variant of interior penalty discontinuous Galerkin method.")
    .declare_key("dg_order", Integer(0,3), Default("1"),
            "Polynomial order for finite element in DG method (order 0 is suitable if there is no diffusion/dispersion).")
    .declare_key("output_fields", Array(EqData::output_selection),
            Default(Model::ModelEqData::default_output_field()),
            "List of fields to write to output file.")

Declare input record type for the equation TransportDG.

Definition at line 188 of file transport_dg.hh.

template<class Model>

LinSys** TransportDG< Model >::ls

private

Linear algebra system for the transport equation.

Definition at line 483 of file transport_dg.hh.

template<class Model>

LinSys* TransportDG< Model >::ls_dt

private

Linear algebra system for the time derivative (actually it is used only for handling the matrix structures).

Definition at line 486 of file transport_dg.hh.

template<class Model>

Mat TransportDG< Model >::mass_matrix

private

The mass matrix.

Definition at line 480 of file transport_dg.hh.

template<class Model>

vector<double> TransportDG< Model >::mm_coef

private

Mass matrix coefficients.

Definition at line 513 of file transport_dg.hh.

template<class Model>

Input::Record TransportDG< Model >::output_rec

private

Record with output specification.

Definition at line 501 of file transport_dg.hh.

template<class Model>

vector<double*> TransportDG< Model >::output_solution

private

Array for storing the output solution data.

Definition at line 495 of file transport_dg.hh.

template<class Model>

OutputTime* TransportDG< Model >::output_stream

private

Definition at line 503 of file transport_dg.hh.

template<class Model>

vector<Vec> TransportDG< Model >::output_vec

private

Vector of solution data.

Definition at line 498 of file transport_dg.hh.

template<class Model>

Vec* TransportDG< Model >::rhs

private

Vector of right hand side.

Definition at line 474 of file transport_dg.hh.

template<class Model>

Mat* TransportDG< Model >::stiffness_matrix

private

The stiffness matrix.

Definition at line 477 of file transport_dg.hh.

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

/home/Jenkins/jenkins/F123-windows32-release/flow123d/src/transport/transport_dg.hh
/home/Jenkins/jenkins/F123-windows32-release/flow123d/src/transport/transport_dg.cc

Classes

Public Types

Public Member Functions

Static Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Model> class TransportDG< Model >

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Model>
class TransportDG< Model >