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

• Published in: Transport in porous media Vol. 91; no. 1; pp. 35 - 47
• Main Authors: Juncu, Gheorghe, Nicola, Aurelian, Popa, Constantin
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2012; Springer; Springer Nature B.V
• Subjects: Civil Engineering; Classical and Continuum Physics; Computer simulation; Discretization; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Exact sciences and technology; Finite volume method; Flow equations; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Infiltration; Multigrid methods; Numerical methods; Porous media; Saturated soils; Soil properties; Two dimensional models; Unsaturated soils; Water flow; Saturated–unsaturated porous media; Richards’ equation; Finite volume; Nonlinear multigrid algorithm; algorithms; models; ground water; Finite volume method; transport; Richards equation; infiltration; unsaturated zone; hydraulics; solution; Saturated-unsaturated porous media; saturated zone; soils; porous media; methodology; Richards' equation
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-011-9831-9

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.