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Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation

Abstract : In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in the numerical simulation of two-phase flows in porous media. The GOE, which occurs when using coupled finite volume schemes on structured grids, is well known to engineers. Several attempts, most of which are of empirical nature, have been put forward in order to alleviate this undesirable phenomenon. Here, our approach relies on a more rigorous notion of angular error for all directions, which in turn enables us via integration and minimization to single out the least anisotropic scheme within a given family of schemes depending on some tuning parameter(s). Numerical test problems testify to the improvement brought by the new construction. grid orientation effect; reservoir simulation; finite volume schemes; nine-point scheme.
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https://hal.archives-ouvertes.fr/hal-02387696
Contributor : Quang Huy Tran <>
Submitted on : Monday, January 4, 2021 - 9:20:57 AM
Last modification on : Tuesday, July 13, 2021 - 3:12:31 PM

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Karine Laurent, Eric Flauraud, Christophe Preux, Quang Huy Tran, Christophe Berthon. Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation. Journal of Computational Physics, Elsevier, 2021, 425, pp.109923. ⟨10.1016/j.jcp.2020.109923⟩. ⟨hal-02387696v2⟩

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