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

#include <dumux/common/properties.hh>
#include <dumux/material/fluidmatrixinteractions/2p/thermalconductivity/somerton.hh>
#include <dumux/material/fluidstates/immiscible.hh>
#include <dumux/porousmediumflow/properties.hh>
#include <dumux/porousmediumflow/immiscible/localresidual.hh>
#include <dumux/porousmediumflow/nonisothermal/model.hh>
#include <dumux/porousmediumflow/nonisothermal/indices.hh>
#include <dumux/porousmediumflow/nonisothermal/iofields.hh>
#include "formulation.hh"
#include "indices.hh"
#include "volumevariables.hh"
#include "iofields.hh"
#include "saturationreconstruction.hh"

Description

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 \(S_n\).

Classes
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...

struct	Dumux::Properties::TTag::TwoP
	The type tag for the isothermal two-phase model. More...

struct	Dumux::Properties::TTag::TwoPNI
	The type tag for the non-isothermal two-phase model. More...

struct	Dumux::Properties::Formulation< TypeTag, TTag::TwoP >
	< Set the default formulation to pwsn More...

struct	Dumux::Properties::LocalResidual< TypeTag, TTag::TwoP >
	Use the immiscible local residual operator for the 2p model. More...

struct	Dumux::Properties::BaseModelTraits< TypeTag, TTag::TwoP >
	The base model traits class. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::TwoP >
	default the actually used traits to the base traits More...

struct	Dumux::Properties::IOFields< TypeTag, TTag::TwoP >
	Set the vtk output fields specific to the twop model. More...

struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::TwoP >
	Set the volume variables property. More...

struct	Dumux::Properties::FluidState< TypeTag, TTag::TwoP >
	The two-phase model uses the immiscible fluid state. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::TwoPNI >
	The non-isothermal model traits class. More...

struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::TwoPNI >
	Set the volume variables property. More...

struct	Dumux::Properties::IOFields< TypeTag, TTag::TwoPNI >
	Set the vtk output fields specific to the non-isothermal twop model. More...

struct	Dumux::Properties::ThermalConductivityModel< TypeTag, TTag::TwoPNI >
	Somerton is used as default model to compute the effective thermal heat conductivity. More...

Namespaces
namespace	Dumux

namespace	Dumux::Properties
	The energy balance equation for a porous solid.

namespace	Dumux::Properties::TTag
	Type tag for numeric models.

Include dependency graph for porousmediumflow/2p/model.hh:

Description

Classes

Namespaces