2p

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

Description

Adaption of the fully implicit scheme to the two-phase flow model.

This model implements two-phase flow of two immiscible fluids \(\alpha \in \{ w, n \}\) using a standard multi-phase Darcy approach as the equation for the conservation of momentum. For details on Darcy's law see dumux/flux/darcyslaw.hh.

By inserting Darcy's law into the equations for the conservation of the phase mass, one gets

\[ \frac{\partial (\phi \varrho_\alpha S_\alpha) }{\partial t} - \nabla \cdot \left\{ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\nabla p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \right\} - q_\alpha = 0, \]

where:

• \( \phi \) is the porosity of the porous medium,
• \( S_\alpha \) represents the saturation of phase \( \alpha \),
• \( \varrho_\alpha \) is the mass density of phase \( \alpha \),
• \( k_{r\alpha} \) is the relative permeability of phase \( \alpha \),
• \( \mu_\alpha \) is the dynamic viscosity of phase \( \alpha \),
• \( \mathbf{K} \) is the intrinsic permeability tensor,
• \( p_\alpha \) is the pressure of phase \( \alpha \),
• \( \mathbf{g} \) is the gravitational acceleration vector,
• \( q_\alpha \) is a source or sink term.

By using constitutive relations for the capillary pressure \(p_c = p_n - p_w\) and relative permeability \(k_{r\alpha}\) and taking advantage of the fact that \(S_w + S_n = 1\), the number of unknowns can be reduced to two. Currently the model supports choosing either \(p_w\) and \(S_n\) or \(p_n\) and \(S_w\) as primary variables. The formulation which ought to be used can be specified by setting the Formulation property to either TwoPFormulation::pwsn or TwoPFormulation::pnsw. By default, the model uses \(p_w\) and \(S_n\).

Files
file	boxmaterialinterfaces.hh
file	formulation.hh
	Defines an enumeration for the formulations accepted by the two-phase model.
file	gridadaptindicator.hh
	Class defining a standard, saturation dependent indicator for grid adaptation.
file	porousmediumflow/2p/griddatatransfer.hh
	Performs the transfer of data on a grid from before to after adaptation.
file	2p/incompressiblelocalresidual.hh
	Element-wise calculation of the residual and its derivatives for a two-phase, incompressible test problem.
file	porousmediumflow/2p/indices.hh
	Defines the indices required for the two-phase fully implicit model.
file	porousmediumflow/2p/iofields.hh
	Adds I/O fields specific to the two-phase model.
file	porousmediumflow/2p/model.hh
	Adaption of the fully implicit scheme to the two-phase flow model.
file	saturationreconstruction.hh
file	porousmediumflow/2p/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the two-phase model.

Classes
class	Dumux::BoxMaterialInterfaces< GridGeometry, PcKrSw >
	Class that determines the material with the lowest capillary pressure (under fully water-saturated conditions) around the nodes of a grid. More...
class	Dumux::TwoPGridAdaptIndicator< TypeTag >
	Class defining a standard, saturation dependent indicator for grid adaptation. More...
class	Dumux::TwoPGridDataTransfer< TypeTag >
	Class performing the transfer of data on a grid from before to after adaptation. More...
class	Dumux::TwoPIncompressibleLocalResidual< TypeTag >
	Element-wise calculation of the residual and its derivatives for a two-phase, incompressible test problem. More...
struct	Dumux::TwoPIndices
	Defines the indices required for the two-phase fully implicit model. More...
class	Dumux::TwoPIOFields
	Adds I/O fields specific to the two-phase model. More...
struct	Dumux::TwoPModelTraits< formulation >
	Specifies a number properties of two-phase models. More...
struct	Dumux::TwoPVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT, SR >
	Traits class for the two-phase model. More...
class	Dumux::TwoPScvSaturationReconstruction< DiscretizationMethod, enableReconstruction >
	Class that computes the nonwetting saturation in an scv from the saturation at the global degree of freedom. More...
class	Dumux::TwoPVolumeVariables< Traits >
	Contains the quantities which are are constant within a finite volume in the two-phase model. More...

Enumerations
enum class	Dumux::TwoPFormulation { Dumux::TwoPFormulation::p0s1 , Dumux::TwoPFormulation::p1s0 }
	Enumerates the formulations which the two-phase model accepts. More...

Enumeration Type Documentation

TwoPFormulation

enum class Dumux::TwoPFormulation

strong

Enumerator
p0s1	first phase pressure and second phase saturation as primary variables
p1s0	first phase saturation and second phase pressure as primary variables