Richards

Richards flow. More...

Description

Richards flow.

In the unsaturated zone, Richards' equation

\[ \frac{\partial\;\phi S_w \varrho_w}{\partial t} - \text{div} \left\lbrace \varrho_w \frac{k_{rw}}{\mu_w} \; \mathbf{K} \; \left( \text{\textbf{grad}} p_w - \varrho_w \textbf{g} \right) \right\rbrace = q_w, \]

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

It can be derived from the two-phase equations, i.e.

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

where \(\alpha \in \{w, n\}\) is the fluid phase, \(\kappa \in \{ w, a \}\) are the components, \(\rho_\alpha\) is the fluid density, \(S_\alpha\) is the fluid saturation, \(\phi\) is the porosity of the soil, \(k_{r\alpha}\) is the relative permeability for the fluid, \(\mu_\alpha\) is the fluid's dynamic viscosity, \(\mathbf{K}\) is the intrinsic permeability, \(p_\alpha\) is the fluid pressure and \(g\) is the potential of the gravity field.

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/richards/indices.hh
	Index names for the Richards model.
file	dumux/porousmediumflow/richards/iofields.hh
	Adds I/O fields specific to the Richards model.
file	porousmediumflow/richards/localresidual.hh
	Element-wise calculation of the Jacobian matrix for problems using the Richards fully implicit models.
file	porousmediumflow/richards/model.hh
	This model implements a variant of the Richards' equation for quasi-twophase flow.
file	porousmediumflow/richards/newtonsolver.hh
	A Richards model Newton solver.
file	richards/primaryvariableswitch.hh
	The primary variable switch for the extended Richards model.
file	porousmediumflow/richards/volumevariables.hh
	Volume averaged quantities required by the Richards model.

Classes
struct	Dumux::RichardsIndices
	Index names for the Richards model. More...
class	Dumux::RichardsIOFields< enableWaterDiffusionInAir >
	Adds I/O fields specific to the Richards model. More...
class	Dumux::RichardsLocalResidual< TypeTag >
	Element-wise calculation of the Jacobian matrix for problems using the Richards fully implicit models. More...
struct	Dumux::RichardsModelTraits< enableDiff >
	Specifies a number properties of the Richards model. More...
struct	Dumux::RichardsVolumeVariablesTraits< PV, FSY, FST, SSY, SST, PT, MT >
	Traits class for the Richards model. More...
class	Dumux::RichardsNewtonSolver< Assembler, LinearSolver >
	A Richards model specific Newton solver. More...
class	Dumux::ExtendedRichardsPrimaryVariableSwitch
	The primary variable switch controlling the phase presence state variable. More...
class	Dumux::RichardsVolumeVariables< Traits >
	Volume averaged quantities required by the Richards model. More...
class	Dumux::RichardsAnalyticalProblem< TypeTag >
	A one-dimensional infiltration problem with a smooth, given solution. More...
class	Dumux::RichardsAnalyticalSpatialParams< GridGeometry, Scalar >
	The spatial parameters for the RichardsAnalyticalProblem. More...
class	Dumux::RichardsWellTracerSpatialParams< GridGeometry, Scalar >
	The spatial parameters for the RichardsWellTracerProblem. More...