porousmediumflow/3p/model.hh File Reference

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

#include <dumux/common/properties.hh>
#include <dumux/material/spatialparams/fv.hh>
#include <dumux/material/fluidstates/immiscible.hh>
#include <dumux/material/fluidmatrixinteractions/3p/thermalconductivitysomerton3p.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 "indices.hh"
#include "volumevariables.hh"
#include "iofields.hh"

Go to the source code of this file.

Description

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

This model implements three-phase flow of three fluid phases \(\alpha \in \{ water, gas, NAPL \}\). The standard multiphase Darcy approach is used 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 equations for the conservation of the phase mass, one gets

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

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.

The model uses commonly applied auxiliary conditions like \(S_w + S_n + S_g = 1\) for the saturations. Furthermore, the phase pressures are related to each other via capillary pressures between the fluid phases, which are functions of the saturation, e.g. according to the approach of Parker et al.

The used primary variables are gas phase pressure \(p_g\), water saturation \(S_w\) and NAPL saturation \(S_n\).

Classes
struct	Dumux::ThreePModelTraits
	Specifies a number properties of three-phase models. More...
struct	Dumux::ThreePVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT >
	Traits class for the two-phase model. More...
struct	Dumux::Properties::TTag::ThreeP
	The type tags for the isothermal three-phase model. More...
struct	Dumux::Properties::TTag::ThreePNI
	The type tags for the non-isothermal three-phase model. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreeP >
	Set the model traits. More...
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::ThreeP >
	The local residual function of the conservation equations. More...
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::ThreeP >
	Set the volume variables property. More...
struct	Dumux::Properties::FluidState< TypeTag, TTag::ThreeP >
	The fluid state which is used by the volume variables to store the thermodynamic state. More...
struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreeP >
	Set the vtk output fields specific to this model. More...
struct	Dumux::Properties::ThermalConductivityModel< TypeTag, TTag::ThreePNI >
	Somerton is used as default model to compute the effective thermal heat conductivity. More...
struct	Dumux::Properties::IOFields< TypeTag, TTag::ThreePNI >
	Set non-isothermal output fields. More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::ThreePNI >
	Set non-isothermal model traits. More...
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::ThreePNI >
	Set the volume variables property. More...

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

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