An adaptive solution strategy for Richards' equation
Stokke, Jakob Seierstad; Mitra, Koondanibha; Storvik, Erlend; Both, Jakub Wiktor; Radu, Florin Adrian
Peer reviewed, Journal article
Published version
Date
2023Metadata
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Original version
Computers and Mathematics with Applications. 2023, 152 155-167. 10.1016/j.camwa.2023.10.020Abstract
Flow in variably saturated porous media is typically modeled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards' equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [1], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical examples.