A study on iterative methods for solving Richards’ equation

By Florian List, Florin Adrian Radu. Computational Geosciences, 2015

257 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e600921ea60367b624da077a0cf04da698d9443d

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In Civil and Structural Engineering

In Computational Mechanics

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Citations in the corpus

On the optimization of the fixed‐stress splitting for Biot's equations (2018, methodology): “ons of Biot’s equations, see [26] for non-linear water compressibility and [29, 30, 31, 32] for unsaturated ow and mechanics. In these cases, one combines a linearization technique, e.g. the L scheme [33, 34] with the splitting algorithm. The convergence of the resulting scheme can be proved rigorou”