Dumux::FVTransport2P2C< TypeTag > Class Template Reference

Compositional transport step in a Finite Volume discretization. More...

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

Inheritance diagram for Dumux::FVTransport2P2C< TypeTag >:

Description

template<class TypeTag>
class Dumux::FVTransport2P2C< TypeTag >

Compositional transport step in a Finite Volume discretization.

The finite volume model for the solution of the transport equation for compositional two-phase flow.

$$\frac{\partial C^\kappa}{\partial t} = - \nabla \cdot \left( \sum_{\alpha} X^{\kappa}_{\alpha} \varrho_{alpha} \bf{v}_{\alpha}\right) + q^{\kappa},$$

where $\bf{v}_{\alpha} = - \lambda_{\alpha} \bf{K} \left(\nabla p_{\alpha} + \rho_{\alpha} \bf{g} \right)$. $p_{\alpha}$ 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. The whole flux contribution for each cell is subdivided into a storage term, a flux term and a source term. Corresponding functions (getFlux() and getFluxOnBoundary()) are provided, internal sources are directly treated.

Template Parameters

TypeTag

The Type Tag

Classes
struct	LocalTimesteppingData

Public Types
using	EntryType = Dune::FieldVector< Scalar, 2 >
using	TimeStepFluxType = Dune::FieldVector< Scalar, 2 >

Public Member Functions
virtual void	update (const Scalar t, Scalar &dt, TransportSolutionType &updateVec, bool impet=false)
	Calculate the update vector and determine timestep size This method calculates the update vector $u$ of the discretized equation. More...
void	updateTransportedQuantity (TransportSolutionType &updateVector)
	Updates the transported quantity once an update is calculated. More...
void	updateTransportedQuantity (TransportSolutionType &updateVector, Scalar dt)
	Updates the transported quantity once an update is calculated. More...
void	updateConcentrations (TransportSolutionType &updateVector, Scalar dt)
	Updates the concentrations once an update is calculated. More...
void	getFlux (ComponentVector &fluxEntries, EntryType &timestepFlux, const Intersection &intersection, CellData &cellDataI)
	Get flux at an interface between two cells The flux through $\gamma$ is calculated according to the underlying pressure field, calculated by the pressure model. More...
void	getFluxOnBoundary (ComponentVector &fluxEntries, EntryType &timestepFlux, const Intersection &intersection, const CellData &cellDataI)
	Get flux on Boundary. More...
void	evalBoundary (GlobalPosition globalPosFace, const Intersection &intersection, FluidState &BCfluidState, PhaseVector &pressBound)
	Evaluate the boundary conditions. More...
void	initialize ()
	Set the initial values before the first pressure equation This method is called before first pressure equation is solved from IMPET. More...
template<class MultiWriter >
void	addOutputVtkFields (MultiWriter &writer)
	Write transport variables into the output files. More...
void	serializeEntity (std::ostream &outstream, const Element &element)
	Function needed for restart option of the transport model: Write out. More...
void	deserializeEntity (std::istream &instream, const Element &element)
	Function needed for restart option of the transport model: Read in. More...

Protected Member Functions
Problem &	problem ()
	Acess function for the current problem. More...
void	innerUpdate (TransportSolutionType &updateVec)

Access functions for protected variables <br>
TransportSolutionType	totalConcentration_
	private vector of transported primary variables More...
Problem &	problem_
bool	impet_
	indicating if we are in an estimate (false) or real impet (true) step. More...
int	averagedFaces_
	number of faces were flux was restricted More...
int	restrictFluxInTransport_
	Restriction of flux on new pressure field if direction reverses from 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...
bool	switchNormals
Scalar	accumulatedDt_
	Current time-interval in sub-time-stepping routine. More...
const Scalar	dtThreshold_
	Threshold for sub-time-stepping routine. More...
std::vector< LocalTimesteppingData >	timeStepData_
	Stores data for sub-time-stepping. More...
Scalar	subCFLFactor_
bool	localTimeStepping_
int	verbosity_
static const int	pressureType = GET_PROP_VALUE(TypeTag, PressureFormulation)
	gives kind of pressure used ( $0 = p_w$, $1 = p_n$, $2 = p_{global}$) More...
void	updatedTargetDt_ (Scalar &dt)
void	resetTimeStepData_ ()
void	getTransportedQuantity (TransportSolutionType &transportedQuantity)
	Return the vector of the transported quantity For an immiscible IMPES scheme, this is the saturation. For compositional simulations, however, the total concentration of all components is transported. More...
Scalar &	totalConcentration (int compIdx, int eIdxGlobal)
	Return the the total concentration stored in the transport vector To get real cell values, do not acess this method, but rather call the respective function in the cell data object. More...
void	getSource (Scalar &update, const Element &element, CellData &cellDataI)
template<class DataEntry >
bool	inPhysicalRange (DataEntry &entry)
	Function to control the abort of the transport-sub-time-stepping depending on a physical parameter range. More...
bool	enableLocalTimeStepping ()
	Function to check if local time stepping is activated. More...
	FVTransport2P2C (Problem &problem)
	Constructs a FVTransport2P2C object Currently, the compositional transport scheme can not be applied with a global pressure / total velocity formulation. More...
virtual	~FVTransport2P2C ()

Member Typedef Documentation

EntryType

template<class TypeTag >

using Dumux::FVTransport2P2C< TypeTag >::EntryType = Dune::FieldVector<Scalar, 2>

Type of the vector of entries

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

TimeStepFluxType

template<class TypeTag >

using Dumux::FVTransport2P2C< TypeTag >::TimeStepFluxType = Dune::FieldVector<Scalar, 2>

Constructor & Destructor Documentation

FVTransport2P2C()

template<class TypeTag >

Dumux::FVTransport2P2C< TypeTag >::FVTransport2P2C ( Problem &  problem )

inline

Constructs a FVTransport2P2C object Currently, the compositional transport scheme can not be applied with a global pressure / total velocity formulation.

Parameters

problem

a problem class object

~FVTransport2P2C()

template<class TypeTag >

virtual Dumux::FVTransport2P2C< TypeTag >::~FVTransport2P2C ( )

inlinevirtual

Member Function Documentation

addOutputVtkFields()

template<class TypeTag >

template<class MultiWriter >

void Dumux::FVTransport2P2C< TypeTag >::addOutputVtkFields ( MultiWriter &  writer )

inline

Write transport variables into the output files.

Parameters

writer

applied VTK-writer

deserializeEntity()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::deserializeEntity ( std::istream &  instream, const Element &  element  )

inline

Function needed for restart option of the transport model: Read in.

enableLocalTimeStepping()

template<class TypeTag >

bool Dumux::FVTransport2P2C< TypeTag >::enableLocalTimeStepping ( )

inline

Function to check if local time stepping is activated.

evalBoundary()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::evalBoundary	(	GlobalPosition	globalPosFace,
		const Intersection &	intersection,
		FluidState &	BCfluidState,
		PhaseVector &	pressBound
	)

Evaluate the boundary conditions.

As the transport primary variable in this formulation is the total component concentration, $C^{\kappa}$ it seems natural that the boundary values are also total concentrations. However, as for the initial conditions, it is possible to define boundaries by means of a saturation. This choice determines which version of flash calculation is necessary to get to the composition at the boundary.

Parameters

globalPosFace	The global position of the face of the current boundary cell
intersection	The current intersection
BCfluidState	FluidState object that is used for the boundary
pressBound	Boundary values of phase pressures

getFlux()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::getFlux	(	ComponentVector &	fluxEntries,
		EntryType &	timestepFlux,
		const Intersection &	intersection,
		CellData &	cellDataI
	)

Get flux at an interface between two cells The flux through $\gamma$ is calculated according to the underlying pressure field, calculated by the pressure model.

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

Here, $\mathbf{d}_{ij}$ is the normalized vector connecting the cell centers, and $\mathbf{n}_{\gamma}$ represents the normal of the face $\gamma$. Due to the nature of the primay Variable, the (volume-)specific total mass concentration, this represents a mass flux per cell volume.

Parameters

fluxEntries	The flux entries, mass influx from cell $j$ to $i$.
timestepFlux	flow velocities for timestep estimation
intersection	The intersection
cellDataI	The cell data for cell $i$

getFluxOnBoundary()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::getFluxOnBoundary	(	ComponentVector &	fluxEntries,
		EntryType &	timestepFlux,
		const Intersection &	intersection,
		const CellData &	cellDataI
	)

Get flux on Boundary.

The flux through $\gamma$ is calculated according to the underlying pressure field, calculated by the pressure model.

$$- A_{\gamma} \mathbf{n}^T_{\gamma} \mathbf{K} \mathbf{d}_{i-Boundary} \sum_{\alpha} \varrho_{\alpha} \lambda_{\alpha} \sum_{\kappa} X^{\kappa}_{\alpha} \left( \frac{p_{\alpha,Boundary}^t - p^{t}_{\alpha,i}}{\Delta x} + \varrho_{\alpha}\mathbf{g}^T \mathbf{d}_{i-Boundary}\right)$$

Here, $\mathbf{u}$ is the normalized vector connecting the cell centers, and $\mathbf{n}_{\gamma_{ij}}$ represents the normal of the face $\gamma{ij}$.

Parameters

fluxEntries	The flux entries, mass influx from cell $j$ to $i$.
timestepFlux	flow velocities for timestep estimation
intersection	The intersection
cellDataI	The cell data for cell $i$

getSource()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::getSource ( Scalar &  update, const Element &  element, CellData &  cellDataI  )

inline

getTransportedQuantity()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::getTransportedQuantity ( TransportSolutionType &  transportedQuantity )

inline

Return the vector of the transported quantity For an immiscible IMPES scheme, this is the saturation. For compositional simulations, however, the total concentration of all components is transported.

Parameters

transportedQuantity

Vector of both transported components

initialize()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::initialize ( )

inline

Set the initial values before the first pressure equation This method is called before first pressure equation is solved from IMPET.

innerUpdate()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::innerUpdate ( TransportSolutionType &  updateVec )

protected

inPhysicalRange()

template<class TypeTag >

template<class DataEntry >

bool Dumux::FVTransport2P2C< TypeTag >::inPhysicalRange ( DataEntry &  entry )

inline

Function to control the abort of the transport-sub-time-stepping depending on a physical parameter range.

Parameters

entry

Cell entries of the update vector

problem()

template<class TypeTag >

Problem & Dumux::FVTransport2P2C< TypeTag >::problem ( )

inlineprotected

Acess function for the current problem.

resetTimeStepData_()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::resetTimeStepData_ ( )

inlineprotected

serializeEntity()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::serializeEntity ( std::ostream &  outstream, const Element &  element  )

inline

Function needed for restart option of the transport model: Write out.

totalConcentration()

template<class TypeTag >

Scalar & Dumux::FVTransport2P2C< TypeTag >::totalConcentration ( int  compIdx, int  eIdxGlobal  )

inline

Return the the total concentration stored in the transport vector To get real cell values, do not acess this method, but rather call the respective function in the cell data object.

Parameters

compIdx	The index of the component
eIdxGlobal	The global index of the current cell.

update()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::update ( const Scalar  t, Scalar &  dt, TransportSolutionType &  updateVec, bool  impet = false  )

virtual

Calculate the update vector and determine timestep size This method calculates the update vector $u$ of the discretized equation.

$$C^{\kappa , new} = C^{\kappa , old} + u,$$

where $u = \sum_{\gamma} \boldsymbol{v}_{\alpha} * \varrho_{\alpha} * X^{\kappa}_{\alpha} * \boldsymbol{n} * A_{\gamma}$, $\boldsymbol{n}$ is the face normal and $A_{\gamma}$ is the face area of face $\gamma$.

In addition to the update vector, the recommended time step size dt is calculated employing a CFL condition.

Parameters

t	Current simulation time $\mathrm{[s]}$
dt	Time step size $\mathrm{[s]}$
updateVec	Update vector, or update estimate for secants, resp. Here in $\mathrm{[kg/m^3]}$
impet	Flag that determines if it is a real impet step or an update estimate for volume derivatives

Reimplemented in Dumux::FV2dTransport2P2CAdaptive< TypeTag >, Dumux::FV3dTransport2P2CAdaptive< TypeTag >, and Dumux::FVTransport2P2CMultiPhysics< TypeTag >.

updateConcentrations()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::updateConcentrations	(	TransportSolutionType &	updateVector,
		Scalar	dt
	)

Updates the concentrations once an update is calculated.

This method updates both, the internal transport solution vector and the entries in the cellData.

Parameters

updateVector	Update vector, or update estimate for secants, resp. Here in $\mathrm{[kg/m^3]}$
dt	Time step size $\mathrm{[s]}$

updatedTargetDt_()

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::updatedTargetDt_ ( Scalar &  dt )

protected

updateTransportedQuantity() [1/2]

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::updateTransportedQuantity

(

TransportSolutionType &

updateVector

)

Updates the transported quantity once an update is calculated.

This method updates both, the internal transport solution vector and the entries in the cellData.

Parameters

updateVector

Update vector, or update estimate for secants, resp. Here in $\mathrm{[kg/m^3]}$

updateTransportedQuantity() [2/2]

template<class TypeTag >

void Dumux::FVTransport2P2C< TypeTag >::updateTransportedQuantity	(	TransportSolutionType &	updateVector,
		Scalar	dt
	)

Updates the transported quantity once an update is calculated.

This method updates both, the internal transport solution vector and the entries in the cellData.

Parameters

updateVector	Update vector, or update estimate for secants, resp. Here in $\mathrm{[kg/m^3]}$
dt	Time step size $\mathrm{[s]}$

Member Data Documentation

accumulatedDt_

template<class TypeTag >

Scalar Dumux::FVTransport2P2C< TypeTag >::accumulatedDt_

protected

Current time-interval in sub-time-stepping routine.

averagedFaces_

template<class TypeTag >

int Dumux::FVTransport2P2C< TypeTag >::averagedFaces_

protected

number of faces were flux was restricted

dtThreshold_

template<class TypeTag >

const Scalar Dumux::FVTransport2P2C< TypeTag >::dtThreshold_

protected

Threshold for sub-time-stepping routine.

impet_

template<class TypeTag >

bool Dumux::FVTransport2P2C< TypeTag >::impet_

protected

indicating if we are in an estimate (false) or real impet (true) step.

localTimeStepping_

template<class TypeTag >

bool Dumux::FVTransport2P2C< TypeTag >::localTimeStepping_

protected

minimalBoundaryPermeability

template<class TypeTag >

Scalar Dumux::FVTransport2P2C< TypeTag >::minimalBoundaryPermeability

protected

Minimal limit for the boundary permeability.

pressureType

template<class TypeTag >

const int Dumux::FVTransport2P2C< TypeTag >::pressureType = GET_PROP_VALUE(TypeTag, PressureFormulation)

staticprotected

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

problem_

template<class TypeTag >

Problem& Dumux::FVTransport2P2C< TypeTag >::problem_

protected

regulateBoundaryPermeability

template<class TypeTag >

bool Dumux::FVTransport2P2C< TypeTag >::regulateBoundaryPermeability

protected

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

restrictFluxInTransport_

template<class TypeTag >

int Dumux::FVTransport2P2C< TypeTag >::restrictFluxInTransport_

protected

Restriction of flux on new pressure field if direction reverses from the pressure equation.

subCFLFactor_

template<class TypeTag >

Scalar Dumux::FVTransport2P2C< TypeTag >::subCFLFactor_

protected

switchNormals

template<class TypeTag >

bool Dumux::FVTransport2P2C< TypeTag >::switchNormals

protected

timeStepData_

template<class TypeTag >

std::vector<LocalTimesteppingData> Dumux::FVTransport2P2C< TypeTag >::timeStepData_

protected

Stores data for sub-time-stepping.

totalConcentration_

template<class TypeTag >

TransportSolutionType Dumux::FVTransport2P2C< TypeTag >::totalConcentration_

protected

private vector of transported primary variables

verbosity_

template<class TypeTag >

int Dumux::FVTransport2P2C< TypeTag >::verbosity_

protected

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

• fvtransport.hh