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/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"

Go to the source code of this file.

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

$$\frac{\partial (\varphi {\varrho }_{\alpha }{S}_{\alpha })}{\partial t}-\mathrm{\nabla }\cdot \left\{{\varrho }_{\alpha }\frac{k_{r\alpha }}{{\mu }_{\alpha }}\mathbf{K}(\mathrm{\nabla }{p}_{\alpha }-{\varrho }_{\alpha }\mathbf{g})\right\}-q_{\alpha }=0,$$

where:

• $\varphi$ 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: