Richards nc

Richards multi-component flow. More...

Description

Richards multi-component flow.

In the unsaturated zone, Richards' equation

\begin{eqnarray*} && \frac{\partial (\sum_w \varrho_w X_w^\kappa \phi S_w )} {\partial t} - \sum_w \text{div} \left\{ \varrho_w X_w^\kappa \frac{k_{rw}}{\mu_w} \mbox{\bf K} (\text{grad}\, p_w - \varrho_{w} \mbox{\bf g}) \right\} \nonumber \\ \nonumber \\ &-& \sum_w \text{div} \left\{{\bf D_{w, pm}^\kappa} \varrho_{w} \text{grad}\, X^\kappa_{w} \right\} - \sum_w q_w^\kappa = 0 \qquad \kappa \in \{w, a,\cdots \} \, , w \in \{w, g\} \end{eqnarray*}

is frequently used to approximate the water distribution above the groundwater level.

In contrast to the full two-phase model, the Richards model assumes gas as the non-wetting fluid and that it exhibits a much lower viscosity than the (liquid) wetting phase. (For example at atmospheric pressure and at room temperature, the viscosity of air is only about \(1\%\) of the viscosity of liquid water.) As a consequence, the \(\frac{k_{r\alpha}}{\mu_\alpha}\) term typically is much larger for the gas phase than for the wetting phase. For this reason, the Richards model assumes that \(\frac{k_{rn}}{\mu_n}\) is infinitely large. This implies that the pressure of the gas phase is equivalent to the static pressure distribution and that therefore, mass conservation only needs to be considered for the wetting phase.

The model thus chooses the absolute pressure of the wetting phase \(p_w\) as its only primary variable. The wetting phase saturation is calculated using the inverse of the capillary pressure, i.e.

\[ S_w = p_c^{-1}(p_n - p_w) \]

holds, where \(p_n\) is a given reference pressure. Nota bene, that the last step is assumes that the capillary pressure-saturation curve can be uniquely inverted, so it is not possible to set the capillary pressure to zero when using the Richards model!

Files
file	porousmediumflow/richardsnc/indices.hh
	Defines the primary variable and equation indices used by the richardsnc model.
file	dumux/porousmediumflow/richardsnc/iofields.hh
	Adds I/O fields specific to the Richards model.
file	porousmediumflow/richardsnc/model.hh
	Base class for all models which use the Richards, n-component fully implicit model.
file	porousmediumflow/richardsnc/volumevariables.hh
	Contains the quantities which are constant within a finite volume in the Richards, n-component model.

Classes
struct	Dumux::RichardsNCIndices
	The indices for the isothermal Richards, n-component model. More...
class	Dumux::RichardsNCIOFields
	Adds I/O fields specific to the Richards model. More...
struct	Dumux::RichardsNCModelTraits< nComp, useMol, repCompEqIdx >
	Specifies a number properties of the Richards n-components model. More...
class	Dumux::RichardsNCVolumeVariables< Traits >
	Contains the quantities which are constant within a finite volume in the Richards, n-component model. More...