extended Richards' equation

extended Richards' equation More...

Description

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

The extended Richards' equation

$$\frac{\partial (\varphi S_w{\varrho }_w)}{\partial t}+\frac{\partial (\varphi (1-S_w){\varrho }_n{X}_n^w)}{\partial t}-\mathrm{\nabla }\cdot \{{\varrho }_w\frac{k_{rw}}{{\mu }_w}\mathbf{K}(\text{nabla}{p}_w-{\varrho }_w\mathbf{\text{g}})+{\mathbf{D}}_{\mathbf{n}\mathbf{,}\mathbf{p}\mathbf{m}}^{\mathbf{w}}{\varrho }_n\mathrm{\nabla }{X}_n^w\}=q_w,$$

where:

• $\varphi$ 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,
• ${\mathbf{D}}_{\mathbf{n}\mathbf{,}\mathbf{p}\mathbf{m}}^{\mathbf{w}}$ 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.

Files
file	porousmediumflow/richardsextended/indices.hh
	Index names for the extended Richards model.
file	porousmediumflow/richardsextended/iofields.hh
	Adds I/O fields specific to the extended Richards model.
file	porousmediumflow/richardsextended/localresidual.hh
	Element-wise calculation of the Jacobian matrix for problems using the extended Richards fully implicit models.
file	porousmediumflow/richardsextended/model.hh
	This model implements a variant of the extended Richards' equation for quasi-twophase flow (see e.g. Vanderborght et al. 2017).
file	richardsextended/primaryvariableswitch.hh
	The primary variable switch for the extended Richards model.
file	porousmediumflow/richardsextended/volumevariables.hh
	Volume averaged quantities required by the extended Richards model.

Classes
struct	Dumux::ExtendedRichardsIndices
	Index names for the extended Richards model. More...
class	Dumux::ExtendedRichardsIOFields
	Adds I/O fields specific to the extended Richards model. More...
class	Dumux::ExtendedRichardsLocalResidual< TypeTag >
	Element-wise calculation of the Jacobian matrix for problems using the extended Richards fully implicit models. More...
struct	Dumux::ExtendedRichardsModelTraits
	Specifies a number properties of the extended Richards model. More...
class	Dumux::ExtendedRichardsVolumeVariables< Traits >
	Volume averaged quantities required by the extended Richards model. More...