2p

Two-phase (immiscible) flow. More...

Description

A two-phase-flow, isothermal pore-network model using the fully implicit scheme.

A mass balance equation is formulated for each pore body $i$ and each phase $\alpha$:

$$V_i\frac{\partial ({\varrho }_{\alpha }{S}_{\alpha }{)}_i}{\partial t}+\sum _j({\varrho }_{\alpha }{Q}_{\alpha }{)}_{ij}=(V{q}_{\alpha }{)}_i.$$

$V_i$ is the pore body volume, and the advective mass flow $({\varrho }_{\alpha }{Q}_{\alpha }{)}_{ij}$ through throat $ij$ can be based on the fluid phase density $\varrho$ either of the upstream pore body $i$ or $j$ (upwinding) or on the respective averaged value. $q_{\alpha }$ is a mass sink or source term defined on pore body $i$.

Per default, the volume flow rate $Q_{\alpha ,ij}$ follows a linear Hagen-Poiseuille-type law (PoreNetworkModel::CreepingFlow) which is only valid for $Re<1$:

$$Q_{\alpha ,ij}=g_{\alpha ,ij}(p_{\alpha ,i}-p_{\alpha ,j}+{\mathrm{\Psi }}_{\alpha }).$$

$g_{\alpha ,ij}$ is a suitable throat conductance value that takes into account the presence/saturation of the individual phases while $p_{\alpha ,i}$ and $p_{\alpha ,j}$ are averaged pore body phase pressures.

The (optional) influence of gravity is given by

$${\mathrm{\Psi }}_{\alpha }={\varrho }_{\alpha }\mathbf{g}({\mathbf{x}}_{\mathbf{i}}-{\mathbf{x}}_{\mathbf{j}}),$$

where ${\mathbf{x}}_{\mathbf{i}}-{\mathbf{x}}_{\mathbf{j}}$ is the distance vector between the centers of pore bodies $i$ and $j$ and $\mathbf{g}$ is the gravitational acceleration.

The primary variables are the wetting phase pressure and the the nonwetting phase saturation ( $p_w$ and $S_n$) or the nonwetting phase pressure and the the wetting phase saturation ( $p_n$ and $S_w$), depending on the chose formulation (see TwoPModel).

Files
file	porenetwork/2p/elementfluxvariablescache.hh
	Element flux variable cache.
file	porenetwork/2p/fluxvariablescache.hh
	Flux variables cache for the two-phase-flow PNM.
file	porenetwork/2p/gridfluxvariablescache.hh
	Global flux variable cache.
file	invasionstate.hh
	Invasion state class for the two-phase PNM.
file	porenetwork/2p/iofields.hh
file	porenetwork/2p/model.hh
	A two-phase-flow, isothermal pore-network model using the fully implicit scheme.
file	newtonconsistencychecks.hh
file	porenetwork/2p/newtonsolver.hh
file	porenetwork/2p/spatialparams.hh
	The two-phase spatial parameters for pore-network models.
file	staticdrainge.hh
	A (quasi-) static two-phase pore-network model for drainage processes.
file	porenetwork/2p/volumevariables.hh

Classes
class	Dumux::PoreNetwork::PNMTwoPElementFluxVariablesCache< GFVC, cachingEnabled >
	The flux variables caches for an element. More...
class	Dumux::PoreNetwork::PNMTwoPElementFluxVariablesCache< GFVC, true >
	The flux variables caches for an element with caching enabled. More...
class	Dumux::PoreNetwork::PNMTwoPElementFluxVariablesCache< GFVC, false >
	The flux variables caches for an element with caching disabled. More...
class	Dumux::PoreNetwork::TwoPFluxVariablesCache< AdvectionType, maxNumCorners >
	Flux variables cache for the two-phase-flow PNM Store data required for flux calculation. More...
struct	Dumux::PoreNetwork::PNMTwoPDefaultGridFVCTraits< P, FVC, IS >
	Flux variable caches traits. More...
class	Dumux::PoreNetwork::PNMTwoPGridFluxVariablesCache< Problem, FluxVariablesCache, cachingEnabled, Traits >
	Flux variable caches on a gridview. More...
class	Dumux::PoreNetwork::PNMTwoPGridFluxVariablesCache< P, FVC, true, Traits >
	The grid flux variables cache for the two-phase PNM hodling the invasion state of the throats. More...
class	Dumux::PoreNetwork::PNMTwoPGridFluxVariablesCache< P, FVC, false, Traits >
	The grid flux variables cache for the two-phase PNM hodling the invasion state of the throats. More...
class	Dumux::PoreNetwork::TwoPInvasionState< P >
	This class updates the invasion state for the two-phase PNM. More...
class	Dumux::PoreNetwork::TwoPIOFields
	Adds output fields specific to the PNM 2p model. More...
class	Dumux::PoreNetwork::TwoPNewtonConsistencyChecks< GridVariables, SolutionVector >
	Consistency checks for the PNM two-phase model. More...
class	Dumux::PoreNetwork::TwoPNewtonSolver< Assembler, LinearSolver, NewtonConsistencyChecks >
	A two-phase PNM specific newton solver. More...
class	Dumux::PoreNetwork::TwoPSpatialParams< GridGeometry, Scalar, LocalRules, Implementation >
	The base class for spatial parameters for pore-network models. More...
class	Dumux::PoreNetwork::TwoPDefaultSpatialParams< GridGeometry, Scalar, LocalRules >
	The default class for spatial parameters for two-phase pore-network models. More...
class	Dumux::PoreNetwork::TwoPStaticDrainage< GridGeometry, Scalar >
	A (quasi-) static two-phase pore-network model for drainage processes. This assumes that there are no pressure gradients within the phases and thus, no flow. More...
class	Dumux::PoreNetwork::TwoPVolumeVariables< Traits >
	Contains the quantities which are are constant within a finite volume (the pore body) in the two-phase model. More...