A mixed MoL-TMoL for the numerical solution of the 2D Richards’ equation in layered soils. (English) Zbl 1459.76115
Summary: 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.
MSC:
| 76M99 | Basic methods in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
discontinuous inteface; implicit method of lines; explicit method of lines; Kirchhoff transform; Filippov dynamical system theoryReferences:
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