Finite volume MPFA L-method discretization of a two-phase flow pressure equation of the sequential IMPES model. More...

#include <dumux/porousmediumflow/2p/sequential/diffusion/mpfa/lmethod/2dpressure.hh>

Inheritance diagram for Dumux::FvMpfaL2dPressure2p< TypeTag >:

Description

template<class TypeTag>
class Dumux::FvMpfaL2dPressure2p< TypeTag >

Finite volume MPFA L-method discretization of a two-phase flow pressure equation of the sequential IMPES model.

Finite volume MPFA L-method discretization of the equations

\[ - \text{div}\, \boldsymbol v_t = - \text{div}\, (\lambda_t \boldsymbol K \textbf{grad}\, \Phi_w + f_n \lambda_t \boldsymbol K \textbf{grad}\, \Phi_{cap} ) = 0, \]

or

\[ - \text{div}\, \boldsymbol v_t = - \text{div}\, (\lambda_t \boldsymbol K \textbf{grad}\, \Phi_n - f_w \lambda_t \boldsymbol K \textbf{grad}\, \Phi_{cap} ) = 0. \]

At Dirichlet boundaries a two-point flux approximation is used.

\[ \Phi = g \; \text{on} \; \Gamma_1, \quad \text{and} \quad -\text{div}\, \boldsymbol v_t \cdot \mathbf{n} = J \; \text{on} \; \Gamma_2. \]

Here, \( \Phi_\alpha \) denotes the potential of phase \( \alpha \), \( \boldsymbol K \) the intrinsic permeability, \( \lambda_t \) the total mobility, \( f_\alpha \) the phase fractional flow function.

More details on the equations can be found in

Wolff 2013: http://elib.uni-stuttgart.de/opus/volltexte/2013/8661/

M. Wolff, Y. Cao, B. Flemisch, R. Helmig, and B. Wohlmuth (2013a). Multi-point flux approximation L-method in 3D: numerical convergence and application to two-phase flow through porous media. In P. Bastian, J. Kraus, R. Scheichl, and M. Wheeler, editors, Simulation of Flow in Porous Media - Applications in Energy and Environment. De Gruyter.

M. Wolff, B. Flemisch, R. Helmig, I. Aavatsmark. Treatment of tensorial relative permeabilities with multipoint flux approximation. International Journal of Numerical Analysis and Modeling (9), pp. 725-744, 2012.

Remark1: only for 2-D quadrilateral grid

Remark2: implemented for UGGrid, ALUGrid, or YaspGrid

Template Parameters

TypeTag The problem Type Tag

Public Types
using	InteractionVolume = FVMPFALInteractionVolume< TypeTag >
	Type of the interaction volume objects. More...

using	TransmissibilityCalculator = FvMpfaL2dTransmissibilityCalculator< TypeTag >

Public Member Functions
void	updateMaterialLaws ()
	constitutive functions are initialized and stored in the variables object More...

void	updateInteractionVolumeInfo ()
	Updates interaction volumes. More...

void	initialize ()
	Initializes the pressure model. More...

void	storePressureSolution ()
	Globally stores the pressure solution. More...

void	storePressureSolution (const Element &element)
	Stores the pressure solution of a cell. More...

void	update ()
	Pressure update. More...

template<class MultiWriter >
void	addOutputVtkFields (MultiWriter &writer)
	Adds pressure output to the output file. More...

	FvMpfaL2dPressure2p (Problem &problem)
	Constructs a FvMpfaL2dPressure2p object. More...

const Scalar	pressure (const int eIdxGlobal) const
	Public access function for the primary pressure variable. More...

void	getSource (EntryType &entry, const Element &element, const CellData &cellData, const bool first)
	Function which calculates the source entry. More...

void	getStorage (EntryType &entry, const Element &element, const CellData &cellData, const bool first)
	Function which calculates the storage entry. More...

void	getFlux (EntryType &entry, const Intersection &intersection, const CellData &cellData, const bool first)
	Function which calculates the flux entry. More...

void	getFluxOnBoundary (EntryType &entry, const Intersection &intersection, const CellData &cellData, const bool first)
	Function which calculates the boundary flux entry. More...

const Matrix &	globalMatrix ()
	Returns the global matrix of the last pressure solution step. More...

const RHSVector &	rightHandSide ()
	Returns the right hand side vector of the last pressure solution step. More...

void	calculateVelocity ()

void	updateVelocity ()

void	serializeEntity (std::ostream &outstream, const Element &element)
	Function for serialization of the pressure field. More...

void	deserializeEntity (std::istream &instream, const Element &element)
	Function for deserialization of the pressure field. More...

void	setFixPressureAtIndex (Scalar pressure, int eIdxGlobal)
	Set a pressure to be fixed at a certain cell. More...

void	unsetFixPressureAtIndex (int eIdxGlobal)
	Reset the fixed pressure state. More...

void	resetFixPressureAtIndex ()

Protected Types
enum	{ rhs = 1 , matrix = 0 }
	Indices of matrix and rhs entries. More...

enum	{ pressEqIdx = Indices::pressureEqIdx }

using	EntryType = Dune::FieldVector< Scalar, 2 >

Protected Member Functions
void	initializeMatrixRowSize ()
	Initialize the global matrix of the system of equations to solve. More...

void	initializeMatrixIndices ()
	Initialize the global matrix of the system of equations to solve. More...

void	assemble (bool first)
	Function which assembles the system of equations to be solved. More...

void	solve ()
	Solves the global system of equations to get the spatial distribution of the pressure. More...

PressureSolution &	pressure ()
	Returns the vector containing the pressure solution. More...

const PressureSolution &	pressure () const
	Returns the vector containing the pressure solution. More...

void	initializePressure ()
	Initialization of the pressure solution vector: Initialization with meaningful values may. More...

Protected Attributes
GlobalInteractionVolumeVector	interactionVolumes_
	Global Vector of interaction volumes. More...

InnerBoundaryVolumeFaces	innerBoundaryVolumeFaces_
	Vector marking faces which intersect the boundary. More...

Matrix	A_
	Global stiffnes matrix (sparse matrix which is build by the `initializeMatrix()` function) More...

RHSVector	f_
	Right hand side vector. More...

Member Typedef Documentation

◆ EntryType

template<class TypeTag >

using Dumux::FVPressure< TypeTag >::EntryType = Dune::FieldVector<Scalar, 2>

protectedinherited

Type of the vector of entries

Contains the return values of the get*()-functions (matrix or right-hand side entry).

◆ InteractionVolume

template<class TypeTag >

using Dumux::FvMpfaL2dPressure2p< TypeTag >::InteractionVolume = FVMPFALInteractionVolume<TypeTag>

Type of the interaction volume objects.

Type of the interaction volume objects used to store the geometric information which is needed to calculated the transmissibility matrices of one MPFA interaction volume.

◆ TransmissibilityCalculator

template<class TypeTag >

using Dumux::FvMpfaL2dPressure2p< TypeTag >::TransmissibilityCalculator = FvMpfaL2dTransmissibilityCalculator<TypeTag>

Member Enumeration Documentation

◆ anonymous enum

template<class TypeTag >

anonymous enum

protectedinherited

Indices of matrix and rhs entries.

During the assembling of the global system of equations get-functions are called (getSource(), getFlux(), etc.), which return global matrix or right hand side entries in a vector. These can be accessed using following indices:

Enumerator
rhs	index for the right hand side entry
matrix	index for the global matrix entry

◆ anonymous enum

template<class TypeTag >

anonymous enum

protectedinherited

Enumerator
pressEqIdx

Constructor & Destructor Documentation

◆ FvMpfaL2dPressure2p()

template<class TypeTag >

Dumux::FvMpfaL2dPressure2p< TypeTag >::FvMpfaL2dPressure2p ( Problem & problem )

inline

Constructs a FvMpfaL2dPressure2p object.

Parameters

problem A problem class object

Member Function Documentation

◆ addOutputVtkFields()

template<class TypeTag >

template<class MultiWriter >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::addOutputVtkFields ( MultiWriter & writer )

inline

Adds pressure output to the output file.

Adds the potential, the potential and the capillary pressure to the output. If the VtkOutputLevel is equal to zero (default) only primary variables are written, if it is larger than zero also secondary variables are written.

Template Parameters

MultiWriter Class defining the output writer

Parameters

writer The output writer (usually a VTKMultiWriter object)

◆ assemble()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::assemble ( bool first )

protectedinherited

Function which assembles the system of equations to be solved.

This function assembles the Matrix and the right hand side (RHS) vector to solve for a pressure field with a Finite-Volume (FV) discretization. Implementations of this base class have to provide the methods getSource(), getStorage(), getFlux() and getFluxOnBoundary() if the assemble() method is called!

Parameters

first Indicates if function is called at the initialization step or during the simulation (If first is true, no pressure field of previous iterations is required)

◆ calculateVelocity()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::calculateVelocity ( )

inlineinherited

◆ deserializeEntity()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::deserializeEntity	(	std::istream &	instream,
		const Element &	element
	)

inlineinherited

Function for deserialization of the pressure field.

Function needed for restart option. Reads the pressure of a grid element from a restart file.

Parameters

instream	Stream from the restart file.
element	Grid element

◆ getFlux()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::getFlux	(	EntryType &	entry,
		const Intersection &	intersection,
		const CellData &	cellData,
		const bool	first
	)

inherited

Function which calculates the flux entry.

Function computes the inter-cell flux term and writes it to the corresponding entry of the entry vector

Parameters

entry	Vector containing return values of the function
intersection	Intersection of two grid elements
cellData	Object containing all model relevant cell data
first	Indicates if function is called in the initialization step or during the simulation

◆ getFluxOnBoundary()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::getFluxOnBoundary	(	EntryType &	entry,
		const Intersection &	intersection,
		const CellData &	cellData,
		const bool	first
	)

inherited

Function which calculates the boundary flux entry.

Function computes the boundary-flux term and writes it to the corresponding entry of the entry vector

Parameters

entry	Vector containing return values of the function
intersection	Intersection of two grid elements
cellData	Object containing all model relevant cell data
first	Indicates if function is called in the initialization step or during the simulation

◆ getSource()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::getSource	(	EntryType &	entry,
		const Element &	element,
		const CellData &	cellData,
		const bool	first
	)

inherited

Function which calculates the source entry.

Function computes the source term and writes it to the corresponding entry of the entry vector

Parameters

entry	Vector containing return values of the function
element	Grid element
cellData	Object containing all model relevant cell data
first	Indicates if function is called in the initialization step or during the simulation

◆ getStorage()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::getStorage	(	EntryType &	entry,
		const Element &	element,
		const CellData &	cellData,
		const bool	first
	)

inherited

Function which calculates the storage entry.

Function computes the storage term and writes it to the corresponding entry of the entry vector

Parameters

entry	Vector containing return values of the function
element	Grid element
cellData	Object containing all model relevant cell data
first	Indicates if function is called in the initialization step or during the simulation

◆ globalMatrix()

template<class TypeTag >

const Matrix & Dumux::FVPressure< TypeTag >::globalMatrix ( )

inlineinherited

Returns the global matrix of the last pressure solution step.

◆ initialize()

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::initialize ( )

inline

Initializes the pressure model.

◆ initializeMatrixIndices()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::initializeMatrixIndices

protectedinherited

Initialize the global matrix of the system of equations to solve.

◆ initializeMatrixRowSize()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::initializeMatrixRowSize

protectedinherited

Initialize the global matrix of the system of equations to solve.

◆ initializePressure()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::initializePressure ( )

inlineprotectedinherited

Initialization of the pressure solution vector: Initialization with meaningful values may.

◆ pressure() [1/3]

template<class TypeTag >

PressureSolution & Dumux::FVPressure< TypeTag >::pressure ( )

inlineprotectedinherited

Returns the vector containing the pressure solution.

◆ pressure() [2/3]

template<class TypeTag >

const PressureSolution & Dumux::FVPressure< TypeTag >::pressure ( ) const

inlineprotectedinherited

Returns the vector containing the pressure solution.

◆ pressure() [3/3]

template<class TypeTag >

const Scalar Dumux::FVPressure< TypeTag >::pressure ( const int eIdxGlobal ) const

inlineinherited

Public access function for the primary pressure variable.

Function returns the cell pressure value at index eIdxGlobal

Parameters

eIdxGlobal Global index of a grid cell

◆ resetFixPressureAtIndex()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::resetFixPressureAtIndex ( )

inlineinherited

◆ rightHandSide()

template<class TypeTag >

const RHSVector & Dumux::FVPressure< TypeTag >::rightHandSide ( )

inlineinherited

Returns the right hand side vector of the last pressure solution step.

◆ serializeEntity()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::serializeEntity	(	std::ostream &	outstream,
		const Element &	element
	)

inlineinherited

Function for serialization of the pressure field.

Function needed for restart option. Writes the pressure of a grid element to a restart file.

Parameters

outstream	Stream into the restart file.
element	Grid element

◆ setFixPressureAtIndex()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::setFixPressureAtIndex	(	Scalar	pressure,
		int	eIdxGlobal
	)

inlineinherited

Set a pressure to be fixed at a certain cell.

Allows to fix a pressure somewhere (at one certain cell) in the domain. This can be necessary e.g. if only Neumann boundary conditions are defined. The pressure is fixed until the unsetFixPressureAtIndex() function is called

Parameters

pressure	Pressure value at eIdxGlobal
eIdxGlobal	Global index of a grid cell

◆ solve()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::solve

protectedinherited

Solves the global system of equations to get the spatial distribution of the pressure.

◆ storePressureSolution() [1/2]

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::storePressureSolution ( )

inline

Globally stores the pressure solution.

◆ storePressureSolution() [2/2]

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::storePressureSolution ( const Element & element )

inline

Stores the pressure solution of a cell.

Parameters

element Dune grid element

◆ unsetFixPressureAtIndex()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::unsetFixPressureAtIndex ( int eIdxGlobal )

inlineinherited

Reset the fixed pressure state.

No pressure is fixed inside the domain until setFixPressureAtIndex() function is called again.

Parameters

eIdxGlobal Global index of a grid cell

◆ update()

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::update ( )

inline

Pressure update.

◆ updateInteractionVolumeInfo()

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::updateInteractionVolumeInfo ( )

inline

Updates interaction volumes.

Globally rebuilds the MPFA interaction volumes.

◆ updateMaterialLaws()

template<class TypeTag >

void Dumux::FvMpfaL2dPressure2p< TypeTag >::updateMaterialLaws

constitutive functions are initialized and stored in the variables object

Updates constitutive relations and stores them in the variable class.

Stores mobility, fractional flow function and capillary pressure for all grid cells.

◆ updateVelocity()

template<class TypeTag >

void Dumux::FVPressure< TypeTag >::updateVelocity ( )

inlineinherited

Member Data Documentation

◆ A_

template<class TypeTag >

Matrix Dumux::FVPressure< TypeTag >::A_

protectedinherited

Global stiffnes matrix (sparse matrix which is build by the initializeMatrix() function)

◆ f_

template<class TypeTag >

RHSVector Dumux::FVPressure< TypeTag >::f_

protectedinherited

Right hand side vector.

◆ innerBoundaryVolumeFaces_

template<class TypeTag >

InnerBoundaryVolumeFaces Dumux::FvMpfaL2dPressure2p< TypeTag >::innerBoundaryVolumeFaces_

protected

Vector marking faces which intersect the boundary.

◆ interactionVolumes_

template<class TypeTag >

GlobalInteractionVolumeVector Dumux::FvMpfaL2dPressure2p< TypeTag >::interactionVolumes_

protected

Global Vector of interaction volumes.

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

lmethod/2dpressure.hh

Description

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Member Typedef Documentation

◆ EntryType

◆ InteractionVolume

◆ TransmissibilityCalculator

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ FvMpfaL2dPressure2p()

Member Function Documentation

◆ addOutputVtkFields()

◆ assemble()

◆ calculateVelocity()

◆ deserializeEntity()

◆ getFlux()

◆ getFluxOnBoundary()

◆ getSource()

◆ getStorage()

◆ globalMatrix()

◆ initialize()

◆ initializeMatrixIndices()

◆ initializeMatrixRowSize()

◆ initializePressure()

◆ pressure() [1/3]

◆ pressure() [2/3]

◆ pressure() [3/3]

◆ resetFixPressureAtIndex()

◆ rightHandSide()

◆ serializeEntity()

◆ setFixPressureAtIndex()

◆ solve()

◆ storePressureSolution() [1/2]

◆ storePressureSolution() [2/2]

◆ unsetFixPressureAtIndex()

◆ update()

◆ updateInteractionVolumeInfo()

◆ updateMaterialLaws()

◆ updateVelocity()

Member Data Documentation

◆ A_

◆ f_

◆ innerBoundaryVolumeFaces_

◆ interactionVolumes_