Keywords: computational hydropedology (hydrology), Richards equation, spatial adaptivity, nonlinear operator treatment, domain decomposition, coarse level, Schwarz domain decomposition, dd-adaptivity, multi-time-step methods.

Modeling the transport processes in a vadose zone plays an important role in predicting the reactions of soil biotopes to anthropogenic activity, for example modeling contaminant transport, the effect of the soil water regime on changes in soil structure and composition, etc. Water flow is governed by the quasilinear Richards equation, while the constitutive laws are typically supplied by the van Genuchten model, which can be understood as a pore size distribution function. This paper is concerned with the implementation of multi-time-step approach for solving the nonlinear Richards equation. When modeling porous media flow in a structured porous medium with Richards equation, the problem typically encounters one major obstacle - it is the determination of the moving wetting front. In order to preserve mass consistency, a stable finite element method approximation of the wetting front typically requires an accurate temporal and spatial integration as a result of the possible convection dominance, and the convergence of the nonlinear solver. The method presented enables the use of an adaptive domain decomposition algorithm together with the multi-time-step treatment of actively changing subdomains.

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