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Robust Newton Solver Based on Variable Switch for a Finite Volume Discretization of Richards Equation

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Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (FVCA 2020)

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Abstract

We propose an efficient nonlinear solver for the resolution of the Richards equation. It is based on variable switching and is easily implemented thanks to a fictitious variable allowing to describe both the saturation and the pressure. Numerical experiments show that our method enables to use Newton’s method with large time steps, reasonable number of iterations and in regions where the pressure-saturation relationship is given by a graph.

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Author information

Authors and Affiliations

  1. IFPEN, 1 & 4, avenue du Bois Préau, 92852, Rueil-Malmaison Cedex, France

    Sabrina Bassetto, Guillaume Enchéry & Quang Huy Tran

  2. Inria, University of Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé, 59000, Lille, France

    Clément Cancès

Authors
  1. Sabrina Bassetto
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  2. Clément Cancès
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  3. Guillaume Enchéry
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  4. Quang Huy Tran
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Corresponding author

Correspondence to Sabrina Bassetto .

Editor information

Editors and Affiliations

  1. NORCE Norwegian Research Centre AS, Bergen, Norway

    Robert Klöfkorn

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Eirik Keilegavlen

  3. Department of Mathematics, University of Bergen, Bergen, Norway

    Florin A. Radu

  4. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

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Bassetto, S., Cancès, C., Enchéry, G., Tran, Q.H. (2020). Robust Newton Solver Based on Variable Switch for a Finite Volume Discretization of Richards Equation. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_35

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