A compositional multi-phase model based on non-linear complementarity functions. More...

#include <ncpmodel.hh>

Inheritance diagram for Ewoms::NcpModel< TypeTag >:

Public Member Functions
	NcpModel (Simulator &simulator)

void	finishInit ()
	Apply the initial conditions to the model. More...

std::string	primaryVarName (int pvIdx) const
	Given an primary variable index, return a human readable name. More...

std::string	eqName (int eqIdx) const
	Given an equation index, return a human readable name. More...

void	updateBegin ()
	Called by the update() method before it tries to apply the newton method. This is primary a hook which the actual model can overload. More...

void	updatePVWeights (const ElementContext &elemCtx) const
	Update the weights of all primary variables within an element given the complete set of intensive quantities. More...

Scalar	primaryVarWeight (int globalDofIdx, int pvIdx) const
	Returns the relative weight of a primary variable for calculating relative errors. More...

Scalar	eqWeight (int globalDofIdx, int eqIdx) const
	Returns the relative weight of an equation. More...

Scalar	minActivityCoeff (int globalDofIdx, int compIdx) const
	Returns the smallest activity coefficient of a component for the most current solution at a vertex. More...

void	registerOutputModules_ ()

bool	phaseIsConsidered (int phaseIdx) const
	Returns true iff a fluid phase is used by the model. More...

void	globalPhaseStorage (EqVector &storage, int phaseIdx)
	Compute the total storage inside one phase of all conservation quantities. More...

Static Public Member Functions
static void	registerParameters ()
	Register all run-time parameters for the immiscible model. More...

static std::string	name ()

Public Attributes
Scalar	referencePressure_

std::vector< ComponentVector >	minActivityCoeff_

Detailed Description

template<class TypeTag>
class Ewoms::NcpModel< TypeTag >

A compositional multi-phase model based on non-linear complementarity functions.

This model implements a $M$ -phase flow of a fluid mixture composed of $N$ chemical species. The phases are denoted by lower index $\alpha \in \{ 1, \dots, M \}$ . All fluid phases are mixtures of $N \geq M - 1$ chemical species which are denoted by the upper index $\kappa \in \{ 1, \dots, N \}$ .

By default, the standard multi-phase Darcy approach is used to determine the velocity, i.e.

$\mathbf{v}_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\mathbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \;,$

although the actual approach which is used can be specified via the FluxModule property. For example, the velocity model can by changed to the Forchheimer approach by

SET_TYPE_PROP(MyProblemTypeTag, FluxModule, Ewoms::ForchheimerFluxModule<TypeTag>);

The core of the model is the conservation mass of each component by means of the equation

$\sum_\alpha \frac{\partial\;\phi c_\alpha^\kappa S_\alpha }{\partial t} - \sum_\alpha \mathrm{div} \left\{ c_\alpha^\kappa \mathbf{v}_\alpha \right\} - q^\kappa = 0 \;.$

For the missing $M$ model assumptions, the model uses non-linear complementarity functions. These are based on the observation that if a fluid phase is not present, the sum of the mole fractions of this fluid phase is smaller than $1$ , i.e.

$\forall \alpha: S_\alpha = 0 \implies \sum_\kappa x_\alpha^\kappa \leq 1$

Also, if a fluid phase may be present at a given spatial location its saturation must be non-negative:

$\forall \alpha: \sum_\kappa x_\alpha^\kappa = 1 \implies S_\alpha \geq 0 *$

Since at any given spatial location, a phase is always either present or not present, one of the strict equalities on the right hand side is always true, i.e.

$\forall \alpha: S_\alpha \left( \sum_\kappa x_\alpha^\kappa - 1 \right) = 0$

always holds.

These three equations constitute a non-linear complementarity problem, which can be solved using so-called non-linear complementarity functions $\Phi(a, b)$ . Such functions have the property

$\Phi(a,b) = 0 \iff a \geq0 \land b \geq0 \land a \cdot b = 0$

Several non-linear complementarity functions have been suggested, e.g. the Fischer-Burmeister function

$\Phi(a,b) = a + b - \sqrt{a^2 + b^2} \;.$

This model uses

$\Phi(a,b) = \min \{a, b \}\;,$

because of its piecewise linearity.

The model assumes local thermodynamic equilibrium and uses the following primary variables:

The pressure of the first phase
The component fugacities $f^1, \dots, f^{N}$
The saturations of the first phases $S_1, \dots, S_{M-1}$
Temperature if the energy equation is enabled

Constructor & Destructor Documentation

template<class TypeTag >

Ewoms::NcpModel< TypeTag >::NcpModel ( Simulator & simulator )

inline

Member Function Documentation

template<class TypeTag >

std::string Ewoms::NcpModel< TypeTag >::eqName ( int eqIdx ) const

inline

Given an equation index, return a human readable name.

Parameters

eqIdx The index of the conservation equation of interest.

template<class TypeTag >

Scalar Ewoms::NcpModel< TypeTag >::eqWeight	(	int	globalDofIdx,
		int	eqIdx
	)		const

inline

Returns the relative weight of an equation.

Parameters

globalVertexIdx	The global index of the vertex
eqIdx	The index of the equation

template<class TypeTag >

void Ewoms::NcpModel< TypeTag >::finishInit ( )

inline

Apply the initial conditions to the model.

References Ewoms::MultiPhaseBaseModel< TypeTag >::finishInit(), and Ewoms::NcpModel< TypeTag >::minActivityCoeff_.

template<class TypeTag >

void Ewoms::MultiPhaseBaseModel< TypeTag >::globalPhaseStorage	(	EqVector &	storage,
		int	phaseIdx
	)

inlineinherited

Compute the total storage inside one phase of all conservation quantities.

Parameters

storage	Stores the total amount of each conserved quantity inside the domain.
phaseIdx	The index of the fluid phase of interest.

References Ewoms::ThreadedEntityIterator< GridView, codim >::beginParallel(), Ewoms::ThreadedEntityIterator< GridView, codim >::increment(), Ewoms::ThreadedEntityIterator< GridView, codim >::isFinished(), Ewoms::ThreadManager< TypeTag >::threadId(), and OmpMutex::unlock().

template<class TypeTag >

Scalar Ewoms::NcpModel< TypeTag >::minActivityCoeff	(	int	globalDofIdx,
		int	compIdx
	)		const

inline

Returns the smallest activity coefficient of a component for the most current solution at a vertex.

Parameters

globalDofIdx	The global index of the vertex (i.e. finite volume) of interest.
compIdx	The index of the component of interest.

References Ewoms::NcpModel< TypeTag >::minActivityCoeff_.

template<class TypeTag >

static std::string Ewoms::NcpModel< TypeTag >::name ( )

inlinestatic

template<class TypeTag >

bool Ewoms::MultiPhaseBaseModel< TypeTag >::phaseIsConsidered ( int phaseIdx ) const

inlineinherited

Returns true iff a fluid phase is used by the model.

Parameters

phaseIdx The index of the fluid phase in question

template<class TypeTag >

std::string Ewoms::NcpModel< TypeTag >::primaryVarName ( int pvIdx ) const

inline

Given an primary variable index, return a human readable name.

Parameters

pvIdx The index of the primary variable of interest.

template<class TypeTag >

Scalar Ewoms::NcpModel< TypeTag >::primaryVarWeight	(	int	globalDofIdx,
		int	pvIdx
	)		const

inline

Returns the relative weight of a primary variable for calculating relative errors.

Parameters

globalDofIdx	The global index of the degree of freedom
pvIdx	The index of the primary variable

References GET_PROP_VALUE, Ewoms::NcpModel< TypeTag >::minActivityCoeff_, and Ewoms::NcpModel< TypeTag >::referencePressure_.

template<class TypeTag >

void Ewoms::NcpModel< TypeTag >::registerOutputModules_ ( )

inline

References Ewoms::MultiPhaseBaseModel< TypeTag >::registerOutputModules_().

template<class TypeTag >

static void Ewoms::NcpModel< TypeTag >::registerParameters ( )

inlinestatic

Register all run-time parameters for the immiscible model.

References Ewoms::VtkDiffusionModule< TypeTag >::registerParameters(), Ewoms::VtkEnergyModule< TypeTag >::registerParameters(), Ewoms::VtkCompositionModule< TypeTag >::registerParameters(), and Ewoms::MultiPhaseBaseModel< TypeTag >::registerParameters().

template<class TypeTag >

void Ewoms::NcpModel< TypeTag >::updateBegin ( )

inline

Called by the update() method before it tries to apply the newton method. This is primary a hook which the actual model can overload.

References Ewoms::NcpModel< TypeTag >::referencePressure_.

template<class TypeTag >

void Ewoms::NcpModel< TypeTag >::updatePVWeights ( const ElementContext & elemCtx ) const

inline

Update the weights of all primary variables within an element given the complete set of intensive quantities.

References Ewoms::NcpModel< TypeTag >::minActivityCoeff_.

Member Data Documentation

template<class TypeTag >

std::vector<ComponentVector> Ewoms::NcpModel< TypeTag >::minActivityCoeff_

mutable

Referenced by Ewoms::NcpModel< TypeTag >::finishInit(), Ewoms::NcpModel< TypeTag >::minActivityCoeff(), Ewoms::NcpModel< TypeTag >::primaryVarWeight(), and Ewoms::NcpModel< TypeTag >::updatePVWeights().

template<class TypeTag >

Scalar Ewoms::NcpModel< TypeTag >::referencePressure_

mutable

Referenced by Ewoms::NcpModel< TypeTag >::primaryVarWeight(), and Ewoms::NcpModel< TypeTag >::updateBegin().

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

ncpmodel.hh

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<class TypeTag> class Ewoms::NcpModel< TypeTag >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class TypeTag>
class Ewoms::NcpModel< TypeTag >