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

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

Inheritance diagram for Dumux::FVPressureCompositional< TypeTag >:

Description

template<class TypeTag>
class Dumux::FVPressureCompositional< TypeTag >

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

Provides the common ground to solve compositional pressure equations of the form

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

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.

Common functions such as output and the initialization procedure are provided here. Also, private vector (the update estimate for the volume derivatives) are stored in this class, as only derived classes (other compositional pressure models) need acess to it. 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	initialMaterialLaws (bool compositional)
	initializes the fluid distribution and hereby the variables container More...

void	initialize (bool solveTwice=false)
	Initializes the simulation run. More...

void	update ()
	Compositional pressure solution routine: update estimate for secants, assemble, solve. More...

void	updateMaterialLaws (bool postTimeStep=false)
	Updates secondary variables. 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...

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	initialize ()
	Initialize pressure model. 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	initializeMatrix ()
	Initialize the global matrix of the system of equations to solve. More...

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

RHSVector	f_
	Right hand side vector. More...

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

Problem &	problem_

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...

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

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

Scalar	ErrorTermUpperBound_

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

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

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

	FVPressureCompositional (Problem &problem)
	Constructs a FVPressureCompositional object. 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).

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

◆ FVPressureCompositional()

template<class TypeTag >

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

inline

Constructs a FVPressureCompositional object.

Parameters

problem a problem class object

Member Function Documentation

◆ addOutputVtkFields()

template<class TypeTag >

template<class MultiWriter >

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

inline

Write data files.

Adds pressure-related quantities, including numerical things such as the volume Error entering the pressure equation. Verobosity of the output can be triggered by the property / parameter VtkOutputLevel, with 0 putting out only primary variables and 4 being very verbose.

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.

◆ initializationOutput()

template<class TypeTag >

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

inline

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::FVPressureCompositional< TypeTag >::initialize ( bool solveTwice = false )

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::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.

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

inline

Compositional pressure solution routine: update estimate for secants, assemble, solve.

An update estime (transport step acoording to old pressure field) determines changes in mass, composition, which is used to calculate volume derivatives entering the pressure equation, as well as an approximate guess for time step size for the storage terms in the p.e. Afterwards, the system is assembled and solved for pressure.

◆ updateMaterialLaws()

template<class TypeTag >

void Dumux::FVPressureCompositional< TypeTag >::updateMaterialLaws ( bool postTimeStep = false )

Updates secondary variables.

A loop through all elements updates the secondary variables stored in the variableclass by using the updated primary variables.

Parameters

postTimeStep Flag indicating method is called from Problem::postTimeStep()

◆ 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
	)

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

◆ updateEstimate_

template<class TypeTag >

TransportSolutionType Dumux::FVPressureCompositional< TypeTag >::updateEstimate_

protected

Update estimate for changes in volume for the pressure equation.

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

fvpressurecompositional.hh

Description

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

general methods for output

Member Typedef Documentation

◆ EntryType

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

Constructor & Destructor Documentation

◆ FVPressureCompositional()

Member Function Documentation

◆ addOutputVtkFields()

◆ assemble()

◆ calculateVelocity()

◆ deserializeEntity()

◆ getFlux()

◆ getFluxOnBoundary()

◆ 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()

◆ unsetFixPressureAtIndex()

◆ update()

◆ updateMaterialLaws()

◆ updateVelocity()

◆ volumeDerivatives()

Member Data Documentation

◆ A_

◆ ErrorTermFactor_

◆ ErrorTermLowerBound_

◆ ErrorTermUpperBound_

◆ f_

◆ incp_

◆ initializationOutputWriter_

◆ maxError_

◆ pressureType

◆ problem_

◆ updateEstimate_