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

#include <transport_dg.hh>

Inheritance diagram for TransportDG< Model >:

Collaboration diagram for TransportDG< Model >:

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Classes
class	EqData

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

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...

bool	evaluate_time_constraint (double &time_constraint)

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

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

	~TransportDG ()
	Destructor. More...

void	initialize () override

void	calculate_cumulative_balance ()

void	calculate_instant_balance ()

const Vec &	get_solution (unsigned int sbi)

double **	get_concentration_matrix ()

void	calculate_concentration_matrix ()

void	update_after_reactions (bool solution_changed)

void	get_par_info (int &el_4_loc, Distribution &el_ds)

int *	get_row_4_el ()

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

Static Public Member Functions
static const Input::Type::Record &	get_input_type ()
	Declare input record type for the equation TransportDG. More...

static const Input::Type::Selection &	get_dg_variant_selection_input_type ()
	Input type for the DG variant selection. More...

Private Member Functions
Model::ModelEqData &	data ()

void	output_vector_gather ()

void	preallocate ()

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...

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...

Vec *	mass_vec
	Mass from previous time instant (necessary when coefficients of mass matrix change in time). 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...

double **	solution_elem_
	Element averages of solution (the array is passed to reactions in operator splitting). More...

Output to file
vector< Vec >	output_vec
	Array for storing the output solution data. More...

Input::Record	input_rec
	Record with input specification. More...

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

vector< vector< double > >	ret_coef
	Retardation coefficient due to sorption. More...

vector< double >	sorption_sources
	Temporary values of source increments. 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...

Static Private Attributes
static const int	registrar
	Registrar of class to factory. More...

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 130 of file transport_dg.hh.

Member Enumeration Documentation

template<class Model >

enum TransportDG::DGVariant

Enumerator
non_symmetric
incomplete
symmetric

Definition at line 149 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 236 of file transport_dg.cc.

template<class Model >

TransportDG< Model >::~TransportDG ( )

Destructor.

Definition at line 363 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 1077 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 946 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 1180 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 714 of file transport_dg.cc.

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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 783 of file transport_dg.cc.

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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 816 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::calculate_concentration_matrix ( )

Definition at line 613 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::calculate_cumulative_balance ( )

Definition at line 673 of file transport_dg.cc.

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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 >

void TransportDG< Model >::calculate_instant_balance ( )

Definition at line 699 of file transport_dg.cc.

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.

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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 1482 of file transport_dg.cc.

template<class Model >

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

inlineprivate

Definition at line 227 of file transport_dg.hh.

template<class Model >

bool TransportDG< Model >::evaluate_time_constraint ( double & time_constraint )

inline

Definition at line 182 of file transport_dg.hh.

template<class Model >

double** TransportDG< Model >::get_concentration_matrix ( )

inline

Definition at line 209 of file transport_dg.hh.

template<class Model >

const Selection & TransportDG< Model >::get_dg_variant_selection_input_type ( )

static

Input type for the DG variant selection.

Definition at line 48 of file transport_dg.cc.

template<class Model >

const Record & TransportDG< Model >::get_input_type ( )

static

Declare input record type for the equation TransportDG.

Definition at line 74 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::get_par_info	(	int *&	el_4_loc,
		Distribution *&	el_ds
	)

Definition at line 1714 of file transport_dg.cc.

template<class Model >

int * TransportDG< Model >::get_row_4_el ( )

Definition at line 1765 of file transport_dg.cc.

template<class Model >

const Vec& TransportDG< Model >::get_solution ( unsigned int sbi )

inline

Definition at line 206 of file transport_dg.hh.

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template<class Model >

void TransportDG< Model >::initialize ( )

override

Definition at line 269 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::output_data ( void )

Postprocesses the solution and writes to output file.

Definition at line 653 of file transport_dg.cc.

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template<class Model >

void TransportDG< Model >::output_vector_gather ( void )

private

Definition at line 397 of file transport_dg.cc.

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template<class Model >

void TransportDG< Model >::preallocate ( )

private

Definition at line 454 of file transport_dg.cc.

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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 1663 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 1293 of file transport_dg.cc.

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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 1603 of file transport_dg.cc.

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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 1501 of file transport_dg.cc.

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template<class Model >

void TransportDG< Model >::set_initial_condition ( )

private

Sets the initial condition.

Definition at line 1638 of file transport_dg.cc.

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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 870 of file transport_dg.cc.

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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 >::update_after_reactions ( bool solution_changed )

Definition at line 1722 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::update_solution ( void )

override

Computes the solution in one time instant.

Definition at line 479 of file transport_dg.cc.

template<class Model >

void TransportDG< Model >::zero_time_step ( )

override

Initialize solution in the zero time.

Definition at line 414 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 482 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 486 of file transport_dg.hh.

template<class Model >

bool TransportDG< Model >::allocation_done

private

Indicates whether matrices have been preallocated.

Definition at line 499 of file transport_dg.hh.

template<class Model >

EqData TransportDG< Model >::data_

private

Field data for model parameters.

Definition at line 405 of file transport_dg.hh.

template<class Model >

unsigned int TransportDG< Model >::dg_order

private

Polynomial order of finite elements.

Definition at line 423 of file transport_dg.hh.

template<class Model >

int TransportDG< Model >::dg_variant

private

DG variant ((non-)symmetric/incomplete.

Definition at line 420 of file transport_dg.hh.

template<class Model >

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

private

Diffusion coefficients.

Definition at line 484 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 488 of file transport_dg.hh.

template<class Model >

FEObjects* TransportDG< Model >::feo

private

Finite element objects.

Definition at line 414 of file transport_dg.hh.

template<class Model >

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

private

Penalty parameters.

Definition at line 417 of file transport_dg.hh.

template<class Model >

Input::Record TransportDG< Model >::input_rec

private

Record with input specification.

Definition at line 466 of file transport_dg.hh.

template<class Model >

LinSys** TransportDG< Model >::ls

private

Linear algebra system for the transport equation.

Definition at line 445 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 448 of file transport_dg.hh.

template<class Model >

Mat* TransportDG< Model >::mass_matrix

private

The mass matrix.

Definition at line 439 of file transport_dg.hh.

template<class Model >

Vec* TransportDG< Model >::mass_vec

private

Mass from previous time instant (necessary when coefficients of mass matrix change in time).

Definition at line 442 of file transport_dg.hh.

template<class Model >

vector<double> TransportDG< Model >::mm_coef

private

Mass matrix coefficients.

Definition at line 476 of file transport_dg.hh.

template<class Model >

vector<Vec> TransportDG< Model >::output_vec

private

Array for storing the output solution data.

Vector of solution data.

Definition at line 463 of file transport_dg.hh.

template<class Model >

const int TransportDG< Model >::registrar

staticprivate

Initial value:

=
        Input::register_class< TransportDG<Model>, Mesh &, const Input::Record>(std::string(Model::ModelEqData::name()) + "_DG") +
        TransportDG<Model>::get_input_type().size()

Registrar of class to factory.

Definition at line 225 of file transport_dg.hh.

template<class Model >

vector<vector<double> > TransportDG< Model >::ret_coef

private

Retardation coefficient due to sorption.

Definition at line 478 of file transport_dg.hh.

template<class Model >

Vec* TransportDG< Model >::rhs

private

Vector of right hand side.

Definition at line 433 of file transport_dg.hh.

template<class Model >

double** TransportDG< Model >::solution_elem_

private

Element averages of solution (the array is passed to reactions in operator splitting).

Definition at line 451 of file transport_dg.hh.

template<class Model >

vector<double> TransportDG< Model >::sorption_sources

private

Temporary values of source increments.

Definition at line 480 of file transport_dg.hh.

template<class Model >

Mat* TransportDG< Model >::stiffness_matrix

private

The stiffness matrix.

Definition at line 436 of file transport_dg.hh.

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

/opt/flow123d/flow123d/src/transport/transport_dg.hh
/opt/flow123d/flow123d/src/transport/transport_dg.cc

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

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 >