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A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods

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Computing and Visualization in Science

Abstract

This paper deals with the 2D system of incompressible poroelasticity equations in which an artificial stabilization term has been added to the discretization on collocated grids. Two issues are discussed: It is proved and shown that the additional term indeed brings stability and does not spoil the second order accurate convergence. Secondly, various smoothers are examined in order to find an optimal multigrid method for the discrete system of equations. Numerical experiments confirm the stability and the second order accuracy, as well as fast multigrid convergence for a realistic poroelasticity experiment.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, University of Zaragoza, Maria de Luna 3, 50018, Zaragoza, Spain

    F. J. Gaspar

  2. Departamento de Matemática Aplicada, University of Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    F. J. Lisbona

  3. Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628, Delft, The Netherlands

    C. W. Oosterlee

Authors
  1. F. J. Gaspar
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  2. F. J. Lisbona
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  3. C. W. Oosterlee
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Correspondence to F. J. Gaspar.

Additional information

Communicated by P. Wesseling.

This research has been partially supported by the INTAS project 03-50-4395, the Spanish project MEC/FEDER MTM 2004-019051, the Diputación General de Aragón and the Dutch program BSIK: knowledge and research capacity, in the ICT project BRICKS (http://www.bsik-bricks.nl), theme MSV1.

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Gaspar, F.J., Lisbona, F.J. & Oosterlee, C.W. A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods. Comput. Visual Sci. 11, 67–76 (2008). https://doi.org/10.1007/s00791-007-0061-1

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  • DOI: https://doi.org/10.1007/s00791-007-0061-1

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