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

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

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.

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...