The finite volume model for the solution of the compositional pressure equation. More...

#include <dumux/porousmediumflow/2p2c/sequential/fv3dpressureadaptive.hh>

Inheritance diagram for Dumux::FV3dPressure2P2CAdaptive< TypeTag >:

Description

template<class TypeTag>
class Dumux::FV3dPressure2P2CAdaptive< TypeTag >

The finite volume model for the solution of the compositional pressure equation.

Provides a Finite Volume implementation for the pressure equation of a compressible system with two components. An IMPES-like method is used for the sequential solution of the problem. Diffusion is neglected, capillarity can be regarded. Isothermal conditions and local thermodynamic equilibrium are assumed. Gravity is included.

\[ c_{total}\frac{\partial p}{\partial t} + \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{\alpha} \bf{v}_{\alpha}\right) = \sum_{\kappa} \frac{\partial v_{total}}{\partial C^{\kappa}} q^{\kappa}, \]

where \(\bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right) \). \( c_{total} \) represents the total compressibility, for constant porosity this yields \( - \frac{\partial V_{total}}{\partial p_{\alpha}} \), \(p_{\alpha} \) denotes the phase pressure, \( \bf{K} \) the absolute permeability, \( \lambda_{\alpha} \) the phase mobility, \( \rho_{\alpha} \) the phase density and \( \bf{g} \) the gravity constant and \( C^{\kappa} \) the total Component concentration. See paper SPE 99619 or "Analysis of a Compositional Model for Fluid Flow in Porous Media" by Chen, Qin and Ewing for derivation.

The pressure base class FVPressure assembles the matrix and right-hand-side vector and solves for the pressure vector, whereas this class provides the actual entries for the matrix and RHS vector. The partial derivatives of the actual fluid volume \( v_{total} \) are gained by using a secant method.

Template Parameters

TypeTag The Type Tag

Public Member Functions
void	update ()

void	initializeMatrix ()
	initializes the matrix to store the system of equations More...

void	initializeMatrixRowSize ()
	Initialize the row sizes of the sparse global matrix. More...

void	initializeMatrixIndices ()
	Determine position of matrix entries. More...

void	initialize (bool solveTwice=false)

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

void	getMpfaFlux (const IntersectionIterator &, const CellData &)
	Compute flux through an irregular interface using a mpfa method. More...

void	get1pMpfaFlux (const IntersectionIterator &, const CellData &)
	Compute single-phase flux through an irregular interface using a mpfa method. More...

void	updateMaterialLaws (bool fromPostTimestep=false)

int	computeTransmissibilities (const IntersectionIterator &, TransmissivityMatrix &, GlobalPosition &, int &, GlobalPosition &, int &)
	Computes the transmissibility coefficients for the MPFA-l method in 3D. More...

void	adaptPressure ()
	Adapt primary variables vector after adapting the grid. More...

	FV3dPressure2P2CAdaptive (Problem &problem)
	Constructs a FVPressure2P2C object. More...

void	get1pSource (EntryType &sourceEntry, const Element &elementI, const CellData &cellDataI)
	Assembles the source term. More...

void	get1pStorage (EntryType &storageEntry, const Element &elementI, CellData &cellDataI)
	Assembles the storage term for a 1p cell in a multiphysics framework. More...

void	get1pFlux (EntryType &entries, const Intersection &intersection, const CellData &cellDataI)
	The compositional single-phase flux in the multiphysics framework. More...

void	get1pFluxOnBoundary (EntryType &entries, const Intersection &intersection, const CellData &cellDataI)
	The compositional single-phase flux in the multiphysics framework. More...

void	initialize ()
	Initialize pressure model. More...

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	update1pMaterialLawsInElement (const Element &elementI, CellData &cellData, bool postTimeStep)
	updates secondary variables of one single phase cell More...

template<class MultiWriter >
void	addOutputVtkFields (MultiWriter &writer)
	Write data files. More...

void	getSource (EntryType &sourceEntry, const Element &elementI, const CellData &cellDataI, const bool first)
	Assembles the source term. More...

void	getStorage (EntryType &storageEntry, const Element &elementI, const CellData &cellDataI, const bool first)
	Assembles the storage term. More...

void	getFlux (EntryType &entries, const Intersection &intersection, const CellData &cellDataI, const bool first)
	Get flux at an interface between two cells. More...

void	getFluxOnBoundary (EntryType &entries, const Intersection &intersection, const CellData &cellDataI, const bool first)
	Get flux on Boundary. More...

void	updateMaterialLawsInElement (const Element &elementI, bool postTimeStep)
	Updates secondary variables of one cell. More...

void	initialMaterialLaws (bool compositional)
	initializes the fluid distribution and hereby the variables container More...

void	volumeDerivatives (const GlobalPosition &, const Element &ep)
	Partial derivatives of the volumes w.r.t. changes in total concentration and pressure. More...

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

using	ElementMapper = typename SolutionTypes::ElementMapper

using	DataHandle = VectorCommDataHandleEqual< ElementMapper, Dune::BlockVector< Dune::FieldVector< int, 1 > >, 0 >

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

enum	{ pressEqIdx = Indices::pressureEqIdx }

Protected Member Functions
int	transmissibilityAdapter_ (const IntersectionIterator &isIt, InteractionVolume &interactionVolume, const int &subVolumeFaceIdx, bool properFluxDirection, Element &additional2, Element &additional3, TransmissivityMatrix &additionalT)
	Adapter to use the general implementation of the mpfa-l for the compositional models. 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
std::map< int, std::vector< int > >	irregularCellMap_
	Container to store all cell's Indice with a hanging node. More...

bool	enableVolumeIntegral_
	Calculates the volume integral (on by default) More...

bool	enableMPFA
	Enables mpfa on hanging nodes (on by default) More...

int	maxInteractionVolumes
	Maximum number of interaction volumes considered (4 by default) More...

InteractionVolumeContainer *	interactionVolumesContainer_
	A pointer to the adaptive interaction volumes container. More...

FvMpfaL3dTransmissibilityCalculator< TypeTag >	mpfal3DTransmissibilityCalculator_
	The common implementation to calculate the Transmissibility with the mpfa-L-method. More...

Dune::BlockVector< Dune::FieldVector< int, 1 > >	nextSubdomain
	vector holding next subdomain More...

const GlobalPosition &	gravity_

Dune::Timer	timer_
	A timer for the time spent on the multiphysics framework. More...

Problem &	problem_

bool	enableVolumeIntegral
	Enables the volume integral of the pressure equation. More...

bool	regulateBoundaryPermeability
	Enables regulation of permeability in the direction of a Dirichlet Boundary Condition. More...

Scalar	minimalBoundaryPermeability
	Minimal limit for the boundary permeability. More...

Scalar	ErrorTermFactor_
	Handling of error term: relaxation factor. More...

Scalar	ErrorTermLowerBound_
	Handling of error term: lower bound for error dampening. More...

Scalar	ErrorTermUpperBound_

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

RHSVector	f_
	Right hand side vector. More...

Static Protected Attributes
static constexpr int	pressureType = getPropValue<TypeTag, Properties::PressureFormulation>()
	gives kind of pressure used ( \( 0 = p_w \), \( 1 = p_n \), \( 2 = p_{global} \)) More...

general methods for output
TransportSolutionType	updateEstimate_
	Update estimate for changes in volume for the pressure equation. More...

VtkMultiWriter< GridView >	initializationOutputWriter_
	output for the initialization procedure More...

Scalar	maxError_
	Maximum volume error of all cells. More...

Scalar	incp_
	Increment for the volume derivative w.r.t pressure. More...

void	initializationOutput (double pseudoTS=0.)
	Write additional debug info in a special writer. More...

Member Typedef Documentation

◆ DataHandle

template<class TypeTag >

using Dumux::FVPressure2P2CMultiPhysics< TypeTag >::DataHandle = VectorCommDataHandleEqual<ElementMapper, Dune::BlockVector<Dune::FieldVector<int, 1> >, 0>

protectedinherited

◆ ElementMapper

template<class TypeTag >

using Dumux::FVPressure2P2CMultiPhysics< TypeTag >::ElementMapper = typename SolutionTypes::ElementMapper

protectedinherited

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

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

◆ FV3dPressure2P2CAdaptive()

template<class TypeTag >

Dumux::FV3dPressure2P2CAdaptive< TypeTag >::FV3dPressure2P2CAdaptive ( Problem & problem )

inline

Constructs a FVPressure2P2C object.

Parameters

problem a problem class object

Member Function Documentation

◆ adaptPressure()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::adaptPressure ( )

inline

Adapt primary variables vector after adapting the grid.

◆ addOutputVtkFields()

template<class TypeTag >

template<class MultiWriter >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::addOutputVtkFields ( MultiWriter & writer )

inlineinherited

Write data files.

Parameters

writer The writer

◆ assemble()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::assemble ( bool first )

function which assembles the system of equations to be solved

This function assembles the Matrix and the RHS vectors to solve for a pressure field with an Finite-Volume Discretization in an implicit fashion. Compared to the method in FVPressure, this implementation calculates fluxes near hanging nodes with the mpfa method using the method getMpfaFlux(). Matrix and Right-hand-side entries are done therein.

Parameters

first Flag if pressure field is unknown

◆ calculateVelocity()

template<class TypeTag >

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

inlineinherited

◆ computeTransmissibilities()

template<class TypeTag >

int Dumux::FV3dPressure2P2CAdaptive< TypeTag >::computeTransmissibilities	(	const IntersectionIterator &	isIt,
		TransmissivityMatrix &	T,
		GlobalPosition &	globalPos4,
		int &	eIdxGlobal4,
		GlobalPosition &	globalPos6,
		int &	eIdxGlobal6
	)

Computes the transmissibility coefficients for the MPFA-l method in 3D.

For faces with a hanging node in 3D, there are four sub-faces. The first subface contains a unique interaction volume, with is directly calculated by this method. For the remainder of the sub-faces, the interaction volumes are build and calculated by the common mpfa-l–implementation of the 2p models. The latter is established via the protected method FV3dPressure2P2CAdaptive::transmissibilityAdapter_(). The calculated Transmissivity Matrices are (along with some geometric information) stored for later use in Variableclass2p2cadaptive .

Parameters

isIt	Iterator to the current intersection
T	Transmissitivity matrix of the first unique interaction volume
globalPos4	Position of the 3rd cell (with local Idx 4) of the unique interaction volume
eIdxGlobal4	Index of the 3rd cell (with local Idx 4) of the unique interaction volume
globalPos6	Position of the 4th cell (with local Idx 6) of the unique interaction volume
eIdxGlobal6	Index of the 4th cell (with local Idx 6) of the unique interaction volume

1) get geometrical information of interaction triangle

2) Calculate omega, chi for matrices

3) Calculate A, B, C, D and solve for T

4) Store and/or calculate additional half edges

◆ deserializeEntity()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< 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

◆ get1pFlux()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::get1pFlux	(	EntryType &	entries,
		const Intersection &	intersection,
		const CellData &	cellDataI
	)

inherited

The compositional single-phase flux in the multiphysics framework.

If only single-phase conditions are encountered, the flux expression simplifies to (written for the case where the wetting phase is only present):

\[ A_{\gamma} \mathbf{n}_{\gamma}^T \mathbf{K} \lambda_w \mathbf{d}_{ij} \left( \frac{p_{w,j}^t - p^{t}_{w,i}}{\Delta x} + \varrho_{w} \mathbf{g}^T \mathbf{d}_{ij} \right) . \]

Parameters

entries	The Matrix and RHS entries
intersection	Intersection between cell I and J
cellDataI	Data of cell I

◆ get1pFluxOnBoundary()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::get1pFluxOnBoundary	(	EntryType &	entries,
		const Intersection &	intersection,
		const CellData &	cellDataI
	)

inherited

The compositional single-phase flux in the multiphysics framework.

If only single-phase conditions are encountered, the flux expression simplifies to (written for the case where the wetting phase is only present):

\[ A_{\gamma} \mathbf{n}_{\gamma}^T \mathbf{K} \varrho_w \lambda_w \mathbf{d}_{i-Boundary} \left( \frac{p_{w,Boundary}^t - p^{t}_{w,i}}{\Delta x} + \varrho_{w} \mathbf{g}^T \mathbf{d}_{i-Boundary} \right) . \]

If a Neumann BC is set, the given (mass-)flux is directly multiplied by the volume derivative and inserted.

Parameters

entries	The Matrix and RHS entries
intersection	Intersection between cell I and J
cellDataI	Data of cell I

◆ get1pMpfaFlux()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::get1pMpfaFlux	(	const IntersectionIterator &	isIt,
		const CellData &	cellDataI
	)

Compute single-phase flux through an irregular interface using a mpfa method.

A mpfa l-method is applied to calculate fluxes near hanging nodes for multiphysics models, using:

\[ - \lambda_{\alpha} \left( \sum_k \tau_{2k} p^t_{\alpha,k} + \varrho_{\alpha} \sum_k \tau_{2k} \mathbf{g}^T \mathbf{x}_{k} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \]

Depending on the applied interaction volumes (e.g. on the boundary only a single interaction volume might be applied), the stencil also spans over neighboring cells. The contribution in other cells than I or J make it necessary that the matrix and rhs entries are filled up within this function.

Parameters

isIt	Iterator of the intersection between cell I and J
cellDataI	Data of cell I

get geometrical Info, transmissibility matrix

compute matrix entry: advective fluxes

◆ get1pSource()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::get1pSource	(	EntryType &	sourceEntry,
		const Element &	elementI,
		const CellData &	cellDataI
	)

inherited

Assembles the source term.

The source is translated into a volumentric source term:

\[ V_i \sum_{\kappa} \frac{1}{\varrho} q^{\kappa}_i \; , \]

because under singlephase conditions

\[ \frac{\partial v_{t}}{\partial C^{\kappa}} \approx \frac{1}{\varrho} \]

.

Parameters

sourceEntry	The Matrix and RHS entries
elementI	The element I
cellDataI	Data of cell I

◆ get1pStorage()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::get1pStorage	(	EntryType &	storageEntry,
		const Element &	elementI,
		CellData &	cellDataI
	)

inherited

Assembles the storage term for a 1p cell in a multiphysics framework.

The storage term comprises the (single-phase) compressibility (due to a change in pressure from last timestep):

\[ V_i c_{i} \frac{p^t_i - p^{t-\Delta t}_i}{\Delta t} \]

and the damped error introduced by the incorrect transport of the last timestep:

\[ V_i \alpha_r \frac{v_{t} - \phi}{\Delta t} \]

. The latter is damped according to Fritz 2011.

Parameters

storageEntry	The Matrix and RHS entries
elementI	The element I
cellDataI	Data of cell I

◆ getFlux()

template<class TypeTag >

void Dumux::FVPressure2P2C< TypeTag >::getFlux	(	EntryType &	entries,
		const Intersection &	intersection,
		const CellData &	cellDataI,
		const bool	first
	)

inherited

Get flux at an interface between two cells.

for first == true, the flux is calculated in traditional fractional-flow forn as in FVPressure2P. for first == false, the flux thorugh \( \gamma \) is calculated via a volume balance formulation

\[ - A_{\gamma} \mathbf{n}^T_{\gamma} \mathbf{K} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \mathbf{d}_{ij} \left( \frac{p_{\alpha,j}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha} \mathbf{g}^T \mathbf{d}_{ij} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \frac{\partial v_{t}}{\partial C^{\kappa}} + V_i \frac{A_{\gamma}}{U_i} \mathbf{d}^T \mathbf{K} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \mathbf{d}_{ij} \left( \frac{p_{\alpha,j}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha} \mathbf{g}^T \mathbf{d}_{ij} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \frac{\frac{\partial v_{t,j}}{\partial C^{\kappa}_j}-\frac{\partial v_{t,i}}{\partial C^{\kappa}_i}}{\Delta x} \]

This includes a boundary integral and a volume integral, because \( \frac{\partial v_{t,i}}{\partial C^{\kappa}_i} \) is not constant. Here, \( \mathbf{d}_{ij} \) is the normalized vector connecting the cell centers, and \( \mathbf{n}_{\gamma} \) represents the normal of the face \( \gamma \).

Parameters

entries	The Matrix and RHS entries
intersection	Intersection between cell I and J
cellDataI	Data of cell I
first	Flag if pressure field is unknown

◆ getFluxOnBoundary()

template<class TypeTag >

void Dumux::FVPressure2P2C< TypeTag >::getFluxOnBoundary	(	EntryType &	entries,
		const Intersection &	intersection,
		const CellData &	cellDataI,
		const bool	first
	)

inherited

Get flux on Boundary.

for first == true, the flux is calculated in traditional fractional-flow forn as in FVPressure2P. for first == false, the flux thorugh \( \gamma \) is calculated via a volume balance formulation

\[ - A_{\gamma} \mathbf{n}^T_{\gamma} \mathbf{K} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \mathbf{d}_{ij} \left( \frac{p_{\alpha,j}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha} \mathbf{g}^T \mathbf{d}_{ij} \right) \sum_{\kappa} \frac{\partial v_{t}}{\partial C^{\kappa}} X^{\kappa}_{\alpha} \;, \]

where we skip the volume integral assuming \( \frac{\partial v_{t,i}}{\partial C^{\kappa}_i} \) to be constant at the boundary. Here, \( \mathbf{d}_{ij} \) is the normalized vector connecting the cell centers, and \( \mathbf{n}_{\gamma} \) represents the normal of the face \( \gamma \).

If a Neumann BC is set, the given (mass-)flux is directly multiplied by the volume derivative and inserted.

Parameters

entries	The Matrix and RHS entries
intersection	Intersection between cell I and J
cellDataI	Data of cell I
first	Flag if pressure field is unknown

◆ getMpfaFlux()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::getMpfaFlux	(	const IntersectionIterator &	isIt,
		const CellData &	cellDataI
	)

Compute flux through an irregular interface using a mpfa method.

A mpfa l-method is applied to calculate fluxes near hanging nodes, using:

\[ - \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \left( \sum_k \tau_{2k} p^t_{\alpha,k} + \varrho_{\alpha} \sum_k \tau_{2k} \mathbf{g}^T \mathbf{x}_{k} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \frac{\partial v_{t}}{\partial C^{\kappa}} + \frac{ V_i}{U_i} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \left( \sum_k \tau_{2k} p^t_{\alpha,k} + \varrho_{\alpha} \sum_k \tau_{2k} \mathbf{g}^T \mathbf{x}_{k} \right) \sum_{\kappa} X^{\kappa}_{\alpha} \frac{\frac{\partial v_{t,j}}{\partial C^{\kappa}_j} -\frac{\partial v_{t,i}}{\partial C^{\kappa}_i}}{\Delta x} \]

Depending on the applied interaction volumes (e.g. on the boundary only a single interaction volume might be applied), the stencil also spans over neighboring cells. The contribution in other cells than I or J make it necessary that the matrix and rhs entries are filled up within this function.

Parameters

isIt	Iterator of the intersection between cell I and J
cellDataI	Data of cell I

◆ getSource()

template<class TypeTag >

void Dumux::FVPressure2P2C< TypeTag >::getSource	(	EntryType &	sourceEntry,
		const Element &	elementI,
		const CellData &	cellDataI,
		const bool	first
	)

inherited

Assembles the source term.

for first == true, a source is implemented as in FVPressure2P. for first == false, the source is translated into a volumentric source term:

\[ V_i \sum_{\kappa} \frac{\partial v_{t}}{\partial C^{\kappa}} q^{\kappa}_i \]

.

Parameters

sourceEntry	The Matrix and RHS entries
elementI	The element I
cellDataI	Data of cell I
first	Flag if pressure field is unknown

◆ getStorage()

template<class TypeTag >

void Dumux::FVPressure2P2C< TypeTag >::getStorage	(	EntryType &	storageEntry,
		const Element &	elementI,
		const CellData &	cellDataI,
		const bool	first
	)

inherited

Assembles the storage term.

for first == true, there is no storage contribution. for first == false, the storage term comprises the compressibility (due to a change in pressure from last timestep):

\[ V_i c_{t,i} \frac{p^t_i - p^{t-\Delta t}_i}{\Delta t} \]

and the damped error introduced by the incorrect transport of the last timestep:

\[ V_i \alpha_r \frac{v_{t} - \phi}{\Delta t} \]

. The latter is damped according to Fritz 2011.

Parameters

storageEntry	The Matrix and RHS entries
elementI	The element I
cellDataI	Data of cell I
first	Flag if pressure field is unknown

◆ globalMatrix()

template<class TypeTag >

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

inlineinherited

Returns the global matrix of the last pressure solution step.

◆ initializationOutput()

template<class TypeTag >

void Dumux::FVPressureCompositional< TypeTag >::initializationOutput ( double pseudoTS = 0. )

inlineinherited

Write additional debug info in a special writer.

To visualize the different steps through the initialization procedure, we use very small pseudo time steps only for the writer! This is only for debugging of the initialization procedure.

Parameters

pseudoTS Time steps that only appear in the writer, not real.

◆ initialize() [1/2]

template<class TypeTag >

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

inlineinherited

Initialize pressure model.

Function initializes the sparse matrix to solve the global system of equations and sets/calculates the initial pressure

◆ initialize() [2/2]

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::initialize ( bool solveTwice = false )

inline

◆ initializeMatrix()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::initializeMatrix

initializes the matrix to store the system of equations

In comparison with the Tpfa method, an mpfa uses a larger flux stencil, hence more matrix entries are required if not only the unique interaction region on the hanging nodes are considered. The method checks weather the additonally regarded cells through mpfa are already "normal" neighbors for fluxes through other interfaces, or if they need to be added.

◆ initializeMatrixIndices()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::initializeMatrixIndices

Determine position of matrix entries.

◆ initializeMatrixRowSize()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::initializeMatrixRowSize

Initialize the row sizes of the sparse global matrix.

◆ initializePressure()

template<class TypeTag >

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

inlineprotectedinherited

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

◆ initialMaterialLaws()

template<class TypeTag >

void Dumux::FVPressureCompositional< TypeTag >::initialMaterialLaws ( bool compositional )

inherited

initializes the fluid distribution and hereby the variables container

It differs from updateMaterialLaws() because there are two possible initial conditions: saturations and concentration.

Parameters

compositional flag that determines if compositional effects are regarded, i.e. a reasonable pressure field is known with which compositions can be calculated.

◆ 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::FVPressure2P2CMultiPhysics< 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.

◆ transmissibilityAdapter_()

template<class TypeTag >

int Dumux::FV3dPressure2P2CAdaptive< TypeTag >::transmissibilityAdapter_	(	const IntersectionIterator &	isIt,
		InteractionVolume &	interactionVolume,
		const int &	subVolumeFaceIdx,
		bool	properFluxDirection,
		Element &	additional2,
		Element &	additional3,
		TransmissivityMatrix &	additionalT
	)

protected

Adapter to use the general implementation of the mpfa-l for the compositional models.

Depending on the subVolumeFaceIdx, the appropriate method in FvMpfaL2dTransmissibilityCalculator (potentially specifying certain cases) gets called and the transmissibility and geometric information of the applied additional cells of the interaction regions are passed back.

Parameters

	isIt	Iterator to the current intersection
	interactionVolume	The current interaction Volume object of interest
	subVolumeFaceIdx	The local index of the intersection of interest in the interaction volume
	properFluxDirection	True if the intersection normal coincides with the local indexing in the interaction volume
[out]	additional2	The 3rd cell's element in the interaction volume
[out]	additional3	The 4th cell's element in the interaction volume
[out]	additionalT	Transmissitivity matrix calculated

◆ 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::FV3dPressure2P2CAdaptive< TypeTag >::update ( )

inline

update of interaction volumes

Todo:: maybe only do this if the grid changed

◆ update1pMaterialLawsInElement()

template<class TypeTag >

void Dumux::FVPressure2P2CMultiPhysics< TypeTag >::update1pMaterialLawsInElement	(	const Element &	elementI,
		CellData &	cellData,
		bool	postTimeStep
	)

inherited

updates secondary variables of one single phase cell

For each element, the secondary variables are updated according to the primary variables. Only a simple flash calulation has to be carried out, as phase distribution is already known: single-phase.

Parameters

elementI	The element
cellData	The cell data of the current element
postTimeStep	Flag indicating if we have just completed a time step

◆ updateMaterialLaws()

template<class TypeTag >

void Dumux::FV3dPressure2P2CAdaptive< TypeTag >::updateMaterialLaws ( bool fromPostTimestep = false )

constitutive functions are updated once if new concentrations are calculated and stored in the variables container

In contrast to the standard sequential 2p2c model, this method also holds routines to adapt the subdomain. The subdomain indicates weather we are in 1p domain (value = 1) or in the two phase subdomain (value = 2). After the grid adaption, update of the subdomain is explicitly avoided.

◆ updateMaterialLawsInElement()

template<class TypeTag >

void Dumux::FVPressure2P2C< TypeTag >::updateMaterialLawsInElement	(	const Element &	element,
		bool	postTimeStep
	)

inherited

Updates secondary variables of one cell.

For each element, the secondary variables are updated according to the primary variables. In case the method is called after the Transport, i.e. at the end / post time step, CellData2p2c.reset() resets the volume derivatives for the next time step.

Parameters

element	The element
postTimeStep	Flag indicating if we have just completed a time step

◆ updateVelocity()

template<class TypeTag >

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

inlineinherited

◆ volumeDerivatives()

template<class TypeTag >

void Dumux::FVPressureCompositional< TypeTag >::volumeDerivatives	(	const GlobalPosition &	globalPos,
		const Element &	element
	)

inherited

Partial derivatives of the volumes w.r.t. changes in total concentration and pressure.

This method calculates the volume derivatives via a secant method, where the secants are gained in a pre-computational step via the transport equation and the last TS size. The partial derivatives w.r.t. mass are defined as \( \frac{\partial v}{\partial C^{\kappa}} = \frac{\partial V}{\partial m^{\kappa}}\)

Parameters

globalPos	The global position of the current element
element	The current element

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)

◆ enableMPFA

template<class TypeTag >

bool Dumux::FV3dPressure2P2CAdaptive< TypeTag >::enableMPFA

protected

Enables mpfa on hanging nodes (on by default)

◆ enableVolumeIntegral

template<class TypeTag >

bool Dumux::FVPressure2P2C< TypeTag >::enableVolumeIntegral

protectedinherited

Enables the volume integral of the pressure equation.

◆ enableVolumeIntegral_

template<class TypeTag >

bool Dumux::FV3dPressure2P2CAdaptive< TypeTag >::enableVolumeIntegral_

protected

Calculates the volume integral (on by default)

◆ ErrorTermFactor_

template<class TypeTag >

Scalar Dumux::FVPressure2P2C< TypeTag >::ErrorTermFactor_

protectedinherited

Handling of error term: relaxation factor.

◆ ErrorTermLowerBound_

template<class TypeTag >

Scalar Dumux::FVPressure2P2C< TypeTag >::ErrorTermLowerBound_

protectedinherited

Handling of error term: lower bound for error dampening.

◆ ErrorTermUpperBound_

template<class TypeTag >

Scalar Dumux::FVPressure2P2C< TypeTag >::ErrorTermUpperBound_

protectedinherited

Handling of error term: upper bound for error dampening

◆ f_

template<class TypeTag >

RHSVector Dumux::FVPressure< TypeTag >::f_

protectedinherited

Right hand side vector.

◆ gravity_

template<class TypeTag >

const GlobalPosition& Dumux::FVPressure2P2CMultiPhysics< TypeTag >::gravity_

protectedinherited

vector including the gravity constant

◆ incp_

template<class TypeTag >

Scalar Dumux::FVPressureCompositional< TypeTag >::incp_

protectedinherited

Increment for the volume derivative w.r.t pressure.

◆ initializationOutputWriter_

template<class TypeTag >

VtkMultiWriter<GridView> Dumux::FVPressureCompositional< TypeTag >::initializationOutputWriter_

protectedinherited

output for the initialization procedure

◆ interactionVolumesContainer_

template<class TypeTag >

InteractionVolumeContainer* Dumux::FV3dPressure2P2CAdaptive< TypeTag >::interactionVolumesContainer_

protected

A pointer to the adaptive interaction volumes container.

◆ irregularCellMap_

template<class TypeTag >

std::map<int, std::vector<int> > Dumux::FV3dPressure2P2CAdaptive< TypeTag >::irregularCellMap_

protected

Container to store all cell's Indice with a hanging node.

◆ maxError_

template<class TypeTag >

Scalar Dumux::FVPressureCompositional< TypeTag >::maxError_

protectedinherited

Maximum volume error of all cells.

◆ maxInteractionVolumes

template<class TypeTag >

int Dumux::FV3dPressure2P2CAdaptive< TypeTag >::maxInteractionVolumes

protected

Maximum number of interaction volumes considered (4 by default)

◆ minimalBoundaryPermeability

template<class TypeTag >

Scalar Dumux::FVPressure2P2C< TypeTag >::minimalBoundaryPermeability

protectedinherited

Minimal limit for the boundary permeability.

◆ mpfal3DTransmissibilityCalculator_

template<class TypeTag >

FvMpfaL3dTransmissibilityCalculator<TypeTag> Dumux::FV3dPressure2P2CAdaptive< TypeTag >::mpfal3DTransmissibilityCalculator_

protected

The common implementation to calculate the Transmissibility with the mpfa-L-method.

◆ nextSubdomain

template<class TypeTag >

Dune::BlockVector<Dune::FieldVector<int,1> > Dumux::FVPressure2P2CMultiPhysics< TypeTag >::nextSubdomain

protectedinherited

vector holding next subdomain

◆ pressureType

template<class TypeTag >

constexpr int Dumux::FVPressure2P2CMultiPhysics< TypeTag >::pressureType = getPropValue<TypeTag, Properties::PressureFormulation>()

staticconstexprprotectedinherited

gives kind of pressure used ( \( 0 = p_w \), \( 1 = p_n \), \( 2 = p_{global} \))

◆ problem_

template<class TypeTag >

Problem& Dumux::FVPressure2P2C< TypeTag >::problem_

protectedinherited

◆ regulateBoundaryPermeability

template<class TypeTag >

bool Dumux::FVPressure2P2C< TypeTag >::regulateBoundaryPermeability

protectedinherited

Enables regulation of permeability in the direction of a Dirichlet Boundary Condition.

◆ timer_

template<class TypeTag >

Dune::Timer Dumux::FVPressure2P2CMultiPhysics< TypeTag >::timer_

protectedinherited

A timer for the time spent on the multiphysics framework.

◆ updateEstimate_

template<class TypeTag >

TransportSolutionType Dumux::FVPressureCompositional< TypeTag >::updateEstimate_

protectedinherited

Update estimate for changes in volume for the pressure equation.

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

fv3dpressureadaptive.hh

Description

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Static Protected Attributes

general methods for output

Member Typedef Documentation

◆ DataHandle

◆ ElementMapper

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ FV3dPressure2P2CAdaptive()

Member Function Documentation

◆ adaptPressure()

◆ addOutputVtkFields()

◆ assemble()

◆ calculateVelocity()

◆ computeTransmissibilities()

◆ deserializeEntity()

◆ get1pFlux()

◆ get1pFluxOnBoundary()

◆ get1pMpfaFlux()

◆ get1pSource()

◆ get1pStorage()

◆ getFlux()

◆ getFluxOnBoundary()

◆ getMpfaFlux()

◆ getSource()

◆ getStorage()

◆ globalMatrix()

◆ initializationOutput()

◆ initialize() [1/2]

◆ initialize() [2/2]

◆ initializeMatrix()

◆ initializeMatrixIndices()

◆ initializeMatrixRowSize()

◆ initializePressure()

◆ initialMaterialLaws()

◆ pressure() [1/3]

◆ pressure() [2/3]

◆ pressure() [3/3]

◆ resetFixPressureAtIndex()

◆ rightHandSide()

◆ serializeEntity()

◆ setFixPressureAtIndex()

◆ solve()

◆ transmissibilityAdapter_()

◆ unsetFixPressureAtIndex()

◆ update()

◆ update1pMaterialLawsInElement()

◆ updateMaterialLaws()

◆ updateMaterialLawsInElement()

◆ updateVelocity()

◆ volumeDerivatives()

Member Data Documentation

◆ A_

◆ enableMPFA

◆ enableVolumeIntegral

◆ enableVolumeIntegral_

◆ ErrorTermFactor_

◆ ErrorTermLowerBound_

◆ ErrorTermUpperBound_

◆ f_

◆ gravity_

◆ incp_

◆ initializationOutputWriter_

◆ interactionVolumesContainer_

◆ irregularCellMap_

◆ maxError_

◆ maxInteractionVolumes

◆ minimalBoundaryPermeability

◆ mpfal3DTransmissibilityCalculator_

◆ nextSubdomain

◆ pressureType

◆ problem_

◆ regulateBoundaryPermeability