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Aspects of Solvers for Large-Scale Coupled Problems in Porous Media

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Abstract

This work summarizes solution strategies for discrete systems occurring in the simulation of processes in the subsurface. The focus is on scalable solvers for large and coupled systems. The goal of this work is to enable researchers to select suitable algorithms and parameter settings to efficiently solve their problems. The work provides an overview of existing methods, highlighting their features, potential, and also frequent pitfalls. Numerical examples are provided for single phase flow, density driven flow and poroelasticity.Aspects of multiphase flow are discussed briefly; a detailed discussion of reactive transport is beyond the scope of the article. Future trends are discussed.

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Notes

  1. Under certain conditions, (1b) becomes inaccurate and is replaced by nonlinear generalizations. In particular, for high velocities, the Forchheimer correction can be used (Bennethum and Giorgi 1997).

  2. Stencil refers to the nonzero entries in a matrix row, e.g., a 5-point 2D stencil can be thought of as the center, North, South, East and West connections.

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Authors and Affiliations

  1. Goethe-Center for Scientific Computing, Goethe-University, Frankfurt, Germany

    Arne Nägel

  2. Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE), King Abdullah University of Science and Technology, Thuwal, Saudi Arabia

    Dmitry Logashenko

  3. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA

    Jacob B. Schroder

  4. Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laboratory, Livermore, CA, USA

    Ulrike M. Yang

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  1. Arne Nägel
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  2. Dmitry Logashenko
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  3. Jacob B. Schroder
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  4. Ulrike M. Yang
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Correspondence to Arne Nägel.

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U.M. Yang: Portions of this work were performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Nägel, A., Logashenko, D., Schroder, J.B. et al. Aspects of Solvers for Large-Scale Coupled Problems in Porous Media. Transp Porous Med 130, 363–390 (2019). https://doi.org/10.1007/s11242-019-01323-w

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