In uniform soils that are susceptible to unstable preferential flow, the water saturation exhibits a nonmonotonic profile upon continuous infiltration. This overshoot cannot be described by the conventional Richards equation. Here, solutions to the infiltrations using a popular nonequilibrium extension to the Richards equation are obtained using the traveling wave nature of the saturation profi...

We analyze regularization schemes for the Richards equation and a time discrete numerical approximation. The original equations can be doubly degenerate, therefore they may exhibit fast and slow diffusion. Additionally, we treat outflow conditions that model an interface separating the porous medium from a free flow domain. In both situations we provide a regularization with a non-degenerate eq...

Both the Canadian Land Surface Scheme (CLASS) and Soil, Vegetation, Snow (SVS) land surface models employ a potentially problematic discretization of Richards equation for unsaturated vertical flow in soil column. It is shown here that this will always overestimate moisture gradient compared to better-constructed first-order scheme, which under some circumstances could lead erroneous drawdown. ...

This paper is concerned with the Richards equation in a heterogeneous domain, each subdomain of which homogeneous and represents rocktype. Our first contribution to rigorously prove convergence toward weak solution cell-centered finite-volume schemes upstream mobility without Kirchhoff’s transform. second numerically demonstrate relevance locally refining grid at interface between subregions, w...