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TP or not TP, that is the question

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Abstract

We give here a comparative study on the mathematical analysis of two (classes of) discretization schemes for the computation of approximate solutions to incompressible two-phase flow problems in homogeneous porous media. The first scheme is the well-known finite volume scheme with a two-point flux approximation, classically used in industry. The second class contains the so-called approximate gradient schemes, which include finite elements with mass lumping, mixed finite elements, and mimetic finite differences. Both (classes of) schemes are nonconforming and can be expressed using discrete function and gradient reconstructions within a variational formulation. Each class has its specific advantages and drawbacks: monotony properties are natural with the two-point finite volume scheme, but meshes are restricted due to consistency issues; on the contrary, gradient schemes can be used on general meshes, but monotony properties are difficult to obtain.

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Authors and Affiliations

  1. L.A.M.A., UMR 8050, Université Paris-Est, Paris, France

    R. Eymard

  2. UMR 7353, LATP, Centrale Marseille, CNRS, Aix-Marseille Université, 13453, Marseille, France

    T. Gallouët & R. Herbin

  3. Team Coffee INRIA Sophia Antipolis Méditerranée, UMR 7351, LJAD, CNRS, University Nice Sophia Antipolis, 06100, Nice, France

    C. Guichard & R. Masson

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  1. R. Eymard
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  2. T. Gallouët
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  3. C. Guichard
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  4. R. Herbin
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  5. R. Masson
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Correspondence to R. Eymard.

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Eymard, R., Gallouët, T., Guichard, C. et al. TP or not TP, that is the question. Comput Geosci 18, 285–296 (2014). https://doi.org/10.1007/s10596-013-9392-9

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  • DOI: https://doi.org/10.1007/s10596-013-9392-9

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