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Nonlinear Multigrid Methods for Numerical Solution of the Unsaturated Flow Equation in Two Space Dimensions

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Abstract

Picard and Newton iterations are widely used to solve numerically the nonlinear Richards’ equation (RE) governing water flow in unsaturated porous media. When solving RE in two space dimensions, direct methods applied to the linearized problem in the Newton/Picard iterations are inefficient. The numerical solving of RE in 2D with a nonlinear multigrid (MG) method that avoids Picard/Newton iterations is the focus of this work. The numerical approach is based on an implicit, second-order accurate time discretization combined with a second-order accurate finite difference spatial discretization. The test problems simulate infiltration of water in 2D unsaturated soils with hydraulic properties described by Broadbridge–White and van Genuchten–Mualem models. The numerical results show that nonlinear MG deserves to be taken into consideration for numerical solving of RE.

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Authors and Affiliations

  1. Catedra Inginerie Chimica, Politehnica University Bucharest, Polizu 1, 011061, Bucharest, Romania

    Gheorghe Juncu

  2. Department of Mathematics, Ovidius University, Bl. Mamaia 124, 900527, Constanta, Romania

    Aurelian Nicola & Constantin Popa

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  1. Gheorghe Juncu
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  2. Aurelian Nicola
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  3. Constantin Popa
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Correspondence to Gheorghe Juncu.

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Juncu, G., Nicola, A. & Popa, C. Nonlinear Multigrid Methods for Numerical Solution of the Unsaturated Flow Equation in Two Space Dimensions. Transp Porous Med 83, 637–652 (2010). https://doi.org/10.1007/s11242-009-9465-3

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  • DOI: https://doi.org/10.1007/s11242-009-9465-3

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