version 3.8
porousmediumflow/richardsextended/model.hh File Reference

This model implements a variant of the extended Richards' equation for quasi-twophase flow (see e.g. Vanderborght et al. 2017). More...

Go to the source code of this file.

Description

The extended Richards' equation

\[ \frac{\partial (\phi S_w \varrho_w) }{\partial t} + \frac{\partial (\phi (1-S_w)\varrho_n X_n^w ) }{\partial t} - \nabla \cdot \left\lbrace \varrho_w \frac{k_{rw}}{\mu_w} \; \mathbf{K} \; \left( \text{\nabla} p_w - \varrho_w \textbf{g} \right) + {\bf D_{n, pm}^w} \varrho_n \nabla X^w_n \right\rbrace = q_w, \]

where:

  • \( \phi \) is the porosity of the porous medium,
  • \( S_w \) represents the saturation of the wetting-phase,
  • \( \varrho_w \) is the mass density of the wetting phase,
  • \( \varrho_n \) is the mass density of the non-wetting phase,
  • \( k_{rw} \) is the relative permeability of the wetting phase,
  • \( \mu_w \) is the dynamic viscosity of the wetting phase,
  • \( \mathbf{K} \) is the intrinsic permeability tensor,
  • \( p_w \) is the pressure of the wetting phase,
  • \( \mathbf{g} \) is the gravitational acceleration vector,
  • \( \bf D_{n,pm}^{w} \) is the effective diffusivity of water in the non-wetting phase,
  • \( X_n^w \) is the mass fraction of water in the non-wetting phase,
  • \( q_w \) is a source or sink term in the wetting phase,

additionally models water vapor diffusion in the gas phase. The model is derived based on the two-phase flow equations based on the assumption that the gas phase does not move but and remains at constant pressure.

Classes

struct  Dumux::ExtendedRichardsModelTraits
 Specifies a number properties of the extended Richards model. More...
 
struct  Dumux::ExtendedRichardsVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT, DT, EDM >
 Traits class for the Richards model. More...
 
struct  Dumux::Properties::TTag::ExtendedRichards
 
struct  Dumux::Properties::TTag::ExtendedRichardsNI
 
struct  Dumux::Properties::LocalResidual< TypeTag, TTag::ExtendedRichards >
 The local residual operator. More...
 
struct  Dumux::Properties::IOFields< TypeTag, TTag::ExtendedRichards >
 Set the vtk output fields specific to this model. More...
 
struct  Dumux::Properties::ModelTraits< TypeTag, TTag::ExtendedRichards >
 The model traits. More...
 
struct  Dumux::Properties::VolumeVariables< TypeTag, TTag::ExtendedRichards >
 Set the volume variables property. More...
 
struct  Dumux::Properties::EffectiveDiffusivityModel< TypeTag, TTag::ExtendedRichards >
 Use the model after Millington (1961) for the effective diffusivity. More...
 
struct  Dumux::Properties::PrimaryVariables< TypeTag, TTag::ExtendedRichards >
 The primary variables vector for the richards model. More...
 
struct  Dumux::Properties::ModelTraits< TypeTag, TTag::ExtendedRichardsNI >
 set non-isothermal model traits More...
 
struct  Dumux::Properties::IOFields< TypeTag, TTag::ExtendedRichardsNI >
 Set the vtk output fields specific to th non-isothermal model. More...
 
struct  Dumux::Properties::VolumeVariables< TypeTag, TTag::ExtendedRichardsNI >
 Set the volume variables property. More...
 
struct  Dumux::Properties::ThermalConductivityModel< TypeTag, TTag::ExtendedRichardsNI >
 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/richardsextended/model.hh: