Solving the nonlinear Richards equation model with adaptive domain decomposition

Solving the nonlinear and nonstationary Richards equation with two-level adaptive domain decomposition (dd-adaptivity)

“…An alternative treatment of a nonlinear problem of this kind can be found in so-called dd-adaptivity (adaptive domain decomposition), as already presented by the authors in [1,2]. The following text will provide a deep explanation of the proposed algorithm, together with some new features that have recently been implemented -mainly the coarse level and subdomain overlap implementation.…”

“…An efficient method for splitting the solutions of nonlinear systems should therefore be time adaptive. Aspects of this problem have already been discussed in Kuraz et al ( , 2014, where the subdomain split resulted in a high number of subdomains. This paper extends our work in the following directions.…”

“…A paper by the authors [2] proposes adaptive domain decomposition based on an additive Schwarz method similar to the algorithm discussed in [17]. The purpose of the current paper is to present an extension of the adaptive domain decomposition method that is referred to as dd-adaptivity.…”

“…These obstacles are the poor conditioning of the system of linear equations arising from its discretization, and the slow convergence or even divergence of the nonlinear operator. We have already discussed this problem in [1,2]. The proposed solution was a method that adaptively splits the computational domain, so that the nonlinear operator always iterates only on small matrices, since the convergence problem of the Richards equation is in most cases only a local problem around the wetting front.…”

Analytical Solution of Richards’ Equation for Application in Automatic Irrigation Systems

“…Water flow is governed by Richards' equations while constitutive laws are typically supplied by the van Genucthen model [2] Over the years, a lot of works have been done in the area of manufacturing and installation of automatic irrigation system but none has been seen in the area of development of a complete analytical model for a real-time automatic irrigation system. Consequently, to adequately design a real-time automatic irrigation system, an accurate analytical model is necessary to facilitate the simulation, prediction and control analysis of the system which largely depends on the development of accurate soil moisture content and plant water uptake models.…”