A study on iterative methods for solving Richards’

Authors: Florian List Florin A Radu

Publish Date: 2016/03/15

Volume: 20, Issue: 2, Pages: 341-353

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Abstract

This work concerns linearization methods for efficiently solving the Richards equation a degenerate ellipticparabolic 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 ie the Newton method the Picard method the Picard/Newton method and the Lscheme 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 Lscheme is theoretically proved and the convergence of the other methods is discussed A new scheme is proposed the Lscheme/Newton method which is more robust and quadratically convergent The linearization methods are tested on illustrative numerical examplesOpen AccessThis article is distributed under the terms of the Creative Commons Attribution 40 International License http//creativecommonsorg/licenses/by/40/ which permits unrestricted use distribution and reproduction in any medium provided you give appropriate credit to the original authors and the source provide a link to the Creative Commons license and indicate if changes were made

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