The finite volume discretization of a saturation transport equation. More...

#include <dumux/porousmediumflow/2p/sequential/transport/cellcentered/saturation.hh>

Inheritance diagram for Dumux::FVSaturation2P< TypeTag >:

Description

template<class TypeTag>
class Dumux::FVSaturation2P< TypeTag >

The finite volume discretization of a saturation transport equation.

This model solves equations of the form

\[ \phi \frac{\partial (\varrho_\alpha S_\alpha)}{\partial t} + \text{div}\, (\varrho_\alpha \boldsymbol{v_\alpha}) = q_\alpha, \]

where \( S_\alpha \) is the saturation of phase \(\alpha \in \{ w, n \}\) and \( \boldsymbol v_\alpha \) is the phase velocity defined by the multi-phase Darcy equation. If a phase velocity is reconstructed from the pressure solution it can be directly inserted into the previous equation. In the incompressible case the equation is further divided by the phase density \( \varrho_\alpha \). If a total velocity is reconstructed the saturation equation is reformulated into:

\[ \phi \frac{\partial S_w}{\partial t} + f_w \text{div}\, \boldsymbol{v}_{t} + f_w \lambda_n \boldsymbol{K}\left(\textbf{grad}\, p_c - (\varrho_n-\varrho_w) {\textbf g} \right)= q_\alpha, \]

to get a wetting phase saturation or

\[ \phi \frac{\partial S_n}{\partial t} + f_n \text{div}\, \boldsymbol{v}_{t} - f_n \lambda_w \boldsymbol{K}\left(\textbf{grad}\, p_c - (\varrho_n-\varrho_w) {\textbf g} \right)= q_\alpha, \]

if the non-wetting phase saturation is the primary transport variable.

The total velocity formulation is only implemented for incompressible fluids and \( f_\alpha \) is the fractional flow function, \( \lambda_\alpha \) is the mobility, \( \boldsymbol K \) the absolute permeability tensor, \( p_c \) the capillary pressure, \( \varrho_\alpha \) the phase density, \( {\textbf g} \) the gravitational acceleration vector, and \( q_\alpha \) the source term.

In the IMPES models the default setting is:

formulation: \( p_w \) - \( S_w \) (Property: Formulation defined as SequentialTwoPCommonIndices::pwsw)

compressibility: disabled (Property: EnableCompressibility set to false)

Template Parameters

TypeTag The Type Tag

Public Member Functions
Velocity &	velocity ()

Velocity &	velocity () const

void	getFlux (Scalar &update, const Intersection &intersection, CellData &cellDataI)
	Function which calculates the flux update. More...

void	getFluxOnBoundary (Scalar &update, const Intersection &intersection, CellData &cellDataI)
	Function which calculates the boundary flux update. More...

void	getSource (Scalar &update, const Element &element, CellData &cellDataI)
	Function which calculates the source update. More...

void	initialize ()
	Sets the initial solution. More...

void	updateMaterialLaws ()
	Update the values of the material laws and constitutive relations. More...

void	getTransportedQuantity (TransportSolutionType &transportedQuantity)
	Writes the current values of the primary transport variable into the `transportedQuantity`-vector (comes as function argument) More...

void	setTransportedQuantity (TransportSolutionType &transportedQuantity)
	Writes the current values of the primary transport variable into the variable container. More...

template<class DataEntry >
bool	inPhysicalRange (DataEntry &entry)
	Check if saturation is in physical range. More...

void	updateTransportedQuantity (TransportSolutionType &updateVec)
	Updates the primary transport variable. More...

void	updateTransportedQuantity (TransportSolutionType &updateVec, Scalar dt)
	Updates the primary transport variable. More...

void	updateSaturationSolution (TransportSolutionType &updateVec)
	Globally updates the saturation solution. More...

void	updateSaturationSolution (TransportSolutionType &updateVec, Scalar dt)
	Globally updates the saturation solution. More...

void	updateSaturationSolution (int eIdxGlobal, Scalar update, Scalar dt)
	Updates the saturation solution of a cell. More...

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

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

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

	FVSaturation2P (Problem &problem)
	Constructs a FVSaturation2P object. More...

void	update (const Scalar t, Scalar &dt, TransportSolutionType &updateVec, bool impet=false)
	Calculate the update vector. More...

void	updateTransport (const Scalar t, Scalar &dt, TransportSolutionType &updateVec)

bool	enableLocalTimeStepping ()

Protected Member Functions
CapillaryFlux &	capillaryFlux ()

const CapillaryFlux &	capillaryFlux () const

GravityFlux &	gravityFlux ()

const GravityFlux &	gravityFlux () const

void	innerUpdate (TransportSolutionType &updateVec)

Constructor & Destructor Documentation

◆ FVSaturation2P()

template<class TypeTag >

Dumux::FVSaturation2P< TypeTag >::FVSaturation2P ( Problem & problem )

inline

Constructs a FVSaturation2P object.

Parameters

problem A problem class object

Member Function Documentation

◆ addOutputVtkFields()

template<class TypeTag >

template<class MultiWriter >

void Dumux::FVSaturation2P< TypeTag >::addOutputVtkFields ( MultiWriter & writer )

inline

Adds saturation output to the output file.

Adds the phase saturation to the output. If the velocity is calculated in the transport model it is also added 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)

◆ capillaryFlux() [1/2]

template<class TypeTag >

CapillaryFlux & Dumux::FVSaturation2P< TypeTag >::capillaryFlux ( )

inlineprotected

◆ capillaryFlux() [2/2]

template<class TypeTag >

const CapillaryFlux & Dumux::FVSaturation2P< TypeTag >::capillaryFlux ( ) const

inlineprotected

◆ deserializeEntity()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::deserializeEntity	(	std::istream &	instream,
		const Element &	element
	)

inline

Function for deserialization of the primary transport variable.

Function needed for restart option. Reads the the primary transport variable of a grid element from a restart file.

Parameters

instream	Stream from the restart file.
element	Grid element

◆ enableLocalTimeStepping()

template<class TypeTag >

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

inlineinherited

◆ getFlux()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::getFlux	(	Scalar &	update,
		const Intersection &	intersection,
		CellData &	cellDataI
	)

Function which calculates the flux update.

Function computes the inter-cell flux term and adds it to the update.

Parameters

update	The cell update
intersection	Intersection of two grid elements
cellDataI	Object containing all model relevant cell data

If a total velocity formulation is used this functions calculates not only the advective flux but also fluxes due to gravity and capillary diffusion. These have to be defined separately as implementation of a DiffusivePart or ConvectivePart (e.g. GravityPart / CapillaryDiffusion ) and added to the property system via properties CapillaryFlux and GravityFlux.

◆ getFluxOnBoundary()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::getFluxOnBoundary	(	Scalar &	update,
		const Intersection &	intersection,
		CellData &	cellDataI
	)

Function which calculates the boundary flux update.

Function computes the boundary-flux term and adds it to the update.

Parameters

update	The cell update
intersection	Intersection of two grid elements
cellDataI	Object containing all model relevant cell data

Dirichlet boundary condition is a phase saturation depending on the formulation ( \( S_w \) (default) or \( S_n \)), Neumann boundary condition are phase mass fluxes ( \( q_w \) (default) or \( q_n \) [ \(\text{kg}/(\text{m}^2 \text{s}\)])

◆ getSource()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::getSource	(	Scalar &	update,
		const Element &	element,
		CellData &	cellDataI
	)

Function which calculates the source update.

Function computes the source term and adds it to the update.

Parameters

update	The cell update
element	Grid element
cellDataI	Object containing all model relevant cell data

Source of the fluid phase has to be defined as mass flux ( \(\text{kg}/(\text{m}^3 \text{s}\)).

◆ getTransportedQuantity()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::getTransportedQuantity ( TransportSolutionType & transportedQuantity )

inline

Writes the current values of the primary transport variable into the transportedQuantity-vector (comes as function argument)

Parameters

transportedQuantity Vector of the size of global numbers of degrees of freedom of the primary transport variable.

◆ gravityFlux() [1/2]

template<class TypeTag >

GravityFlux & Dumux::FVSaturation2P< TypeTag >::gravityFlux ( )

inlineprotected

◆ gravityFlux() [2/2]

template<class TypeTag >

const GravityFlux & Dumux::FVSaturation2P< TypeTag >::gravityFlux ( ) const

inlineprotected

◆ initialize()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::initialize

Sets the initial solution.

Sets the initial solution \( S_0 \).

◆ innerUpdate()

template<class TypeTag >

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

protectedinherited

◆ inPhysicalRange()

template<class TypeTag >

template<class DataEntry >

bool Dumux::FVSaturation2P< TypeTag >::inPhysicalRange ( DataEntry & entry )

inline

Check if saturation is in physical range.

Template Parameters

DataEntry Data class

Parameters

entry Entry which is checked

◆ serializeEntity()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::serializeEntity	(	std::ostream &	outstream,
		const Element &	element
	)

inline

Function for serialization of the primary transport variable.

Function needed for restart option. Writes the primary transport variable of a grid element to a restart file.

Parameters

outstream	Stream into the restart file.
element	Grid element

◆ setTransportedQuantity()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::setTransportedQuantity ( TransportSolutionType & transportedQuantity )

inline

Writes the current values of the primary transport variable into the variable container.

Parameters

transportedQuantity Vector of the size of global numbers of degrees of freedom of the primary transport variable.

◆ update()

template<class TypeTag >

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

inherited

Calculate the update vector.

Parameters

t	current time
dt	time step size
updateVec	vector containing the update values
impet	variable should be true if an impet algorithm is used and false if the transport part is solved independently

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

◆ updateMaterialLaws()

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateMaterialLaws

Update the values of the material laws and constitutive relations.

Updates constitutive relations and stores them in the variable class.

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

◆ updateSaturationSolution() [1/3]

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateSaturationSolution	(	int	eIdxGlobal,
		Scalar	update,
		Scalar	dt
	)

inline

Updates the saturation solution of a cell.

Calculates secondary saturation variables and stores saturations.

Parameters

eIdxGlobal	Global cell index
update	Cell saturation update
dt	Current time step

◆ updateSaturationSolution() [2/3]

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateSaturationSolution ( TransportSolutionType & updateVec )

inline

Globally updates the saturation solution.

Parameters

updateVec Vector containing the global update.

◆ updateSaturationSolution() [3/3]

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateSaturationSolution	(	TransportSolutionType &	updateVec,
		Scalar	dt
	)

inline

Globally updates the saturation solution.

Parameters

updateVec	Vector containing the global update.
dt	time step for update

◆ updateTransport()

template<class TypeTag >

void Dumux::FVTransport< TypeTag >::updateTransport	(	const Scalar	t,
		Scalar &	dt,
		TransportSolutionType &	updateVec
	)

inlineinherited

◆ updateTransportedQuantity() [1/2]

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateTransportedQuantity ( TransportSolutionType & updateVec )

inline

Updates the primary transport variable.

Parameters

updateVec Vector containing the global update.

◆ updateTransportedQuantity() [2/2]

template<class TypeTag >

void Dumux::FVSaturation2P< TypeTag >::updateTransportedQuantity	(	TransportSolutionType &	updateVec,
		Scalar	dt
	)

inline

Updates the primary transport variable.

Parameters

updateVec	Vector containing the global update
dt	time step for update

◆ velocity() [1/2]

template<class TypeTag >

Velocity & Dumux::FVSaturation2P< TypeTag >::velocity ( )

inline

◆ velocity() [2/2]

template<class TypeTag >

Velocity & Dumux::FVSaturation2P< TypeTag >::velocity ( ) const

inline

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

saturation.hh

Description

Public Member Functions

Protected Member Functions

Constructor & Destructor Documentation

◆ FVSaturation2P()

Member Function Documentation

◆ addOutputVtkFields()

◆ capillaryFlux() [1/2]

◆ capillaryFlux() [2/2]

◆ deserializeEntity()

◆ enableLocalTimeStepping()

◆ getFlux()

◆ getFluxOnBoundary()

◆ getSource()

◆ getTransportedQuantity()

◆ gravityFlux() [1/2]

◆ gravityFlux() [2/2]

◆ initialize()

◆ innerUpdate()

◆ inPhysicalRange()

◆ serializeEntity()

◆ setTransportedQuantity()

◆ update()

◆ updateMaterialLaws()

◆ updateSaturationSolution() [1/3]

◆ updateSaturationSolution() [2/3]

◆ updateSaturationSolution() [3/3]

◆ updateTransport()

◆ updateTransportedQuantity() [1/2]

◆ updateTransportedQuantity() [2/2]

◆ velocity() [1/2]

◆ velocity() [2/2]