A study on iterative methods for solving Richards’ equation

• Published in: Computational geosciences Vol. 20; no. 2; pp. 341 - 353
• Main Authors: List, Florian, Radu, Florin A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2016; Springer Nature B.V
• Subjects: Computation; Computational mathematics; Convergence; Earth and Environmental Science; Earth Sciences; Fluid mechanics; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Linear systems; Linearization; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Newton methods; Original Paper; Porous materials; Porous media; Soil Science & Conservation; Linearization schemes; Richards’ equation; Galerkin finite elements; Flow in porous media; Picard method; Newton method; Convergence analysis
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-016-9566-3

This work concerns linearization methods for efficiently solving the Richards equation, a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media. The discretization of Richards’ equation is based on backward Euler in time and Galerkin finite elements in space. The most valuable linearization schemes for Richards’ equation, i.e. the Newton method, the Picard method, the Picard/Newton method and the L -scheme are presented and their performance is comparatively studied. The convergence, the computational time and the condition numbers for the underlying linear systems are recorded. The convergence of the L -scheme is theoretically proved and the convergence of the other methods is discussed. A new scheme is proposed, the L -scheme/Newton method which is more robust and quadratically convergent. The linearization methods are tested on illustrative numerical examples.