A mixed MoL-TMoL for the numerical solution of the 2D Richards' equation in layered soils

Water infiltration into layered soils is studied, considering a two dimensional spatial domain. The focus is on the treatment of discontinuity at the intersection of non-overlapping soils. The novelty of this paper is based on a mixed MoL-TMoL, which merges desirable features of both Method of Lines (MoL) and Transversal Method of Lines (TMoL); such a numerical approach allows us the numerical treatment of the solution at the discontinuous interfaces by means of Filippov theory for dynamical systems. Numerical simulations, based on implicit and semi-implicit schemes of low accuracy, are provided for validating this approach.