porousmediumflow/2p/model.hh File Reference

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

#include <dumux/common/properties.hh>
#include <dumux/material/fluidmatrixinteractions/2p/thermalconductivitysomerton.hh>
#include <dumux/material/fluidstates/immiscible.hh>
#include <dumux/material/spatialparams/fv.hh>
#include <dumux/porousmediumflow/properties.hh>
#include <dumux/porousmediumflow/1p/model.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"

Go to the source code of this file.

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, i.e.

\[ v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \textbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} {\textbf g} \right) \]

By inserting this into the equation for the conservation of the phase mass, one gets

\[ \phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t} - \text{div} \left\{ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mbox{\bf g} \right) \right\} - q_\alpha = 0 \;, \]

All equations are discretized using a vertex-centered finite volume (box) or cell-centered finite volume scheme as spatial and the implicit Euler method as time discretization.

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

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