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3.3.0
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.3.0
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Base class for all models which use the Richards, n-component fully implicit model. More...
#include <dumux/common/properties.hh>#include <dumux/material/spatialparams/fv1p.hh>#include <dumux/material/fluidmatrixinteractions/diffusivitymillingtonquirk.hh>#include <dumux/material/fluidmatrixinteractions/1p/thermalconductivityaverage.hh>#include <dumux/material/components/simpleh2o.hh>#include <dumux/material/components/constant.hh>#include <dumux/material/fluidsystems/liquidphase2c.hh>#include <dumux/material/fluidstates/compositional.hh>#include <dumux/porousmediumflow/properties.hh>#include <dumux/porousmediumflow/nonisothermal/model.hh>#include <dumux/porousmediumflow/nonisothermal/indices.hh>#include <dumux/porousmediumflow/nonisothermal/iofields.hh>#include <dumux/porousmediumflow/compositional/localresidual.hh>#include <dumux/porousmediumflow/richards/model.hh>#include "volumevariables.hh"#include "indices.hh"#include "iofields.hh"Go to the source code of this file.
Base class for all models which use the Richards, n-component fully implicit model.
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} \mathbf{K} (\text{grad}\, p_w - \varrho_{w} \mathbf{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 nonwetting 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!
Namespaces | |
| namespace | Dumux |
| namespace | Dumux::Properties |
| namespace | Dumux::Properties::TTag |
| Type tag for numeric models. | |
1.9.3