Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures

JOURNAL OF COMPUTATIONAL PHYSICS

卷:407

Article

Ghilani, Mustapha¹  Quenjel, El Houssaine^2,3  Saad, Mazen⁴ 

[1] Moulay Ismail Univ, ENSAM, BP 15290 EL Mansour, Meknes 50500, Morocco

[2] Univ Nice Sophia Antipolis, CNRS, UMR 7351, LJAD, Parc Valrose, F-06108 Nice 02, France

[3] Univ Nice Sophia Antipolis, COFFEE Team, INRIA Sophia Antipolis Meediterranee, Parc Valrose, F-06108 Nice 02, France

[4] Ecole Cent Nantes, LMJL, CNRS, UMR 6629, 1 Rue Noe, F-44321 Nantes, France

关键词: Positivity-preserving;    Finite volume;    Anisotropic;    Porous media;    Convergence;   

DOI  :  10.1016/j.jcp.2020.109233

来源: Elsevier

【 摘 要 】

We are concerned with the approximation of solutions to a compressible two-phase flow model in porous media thanks to an enhanced control volume finite element discretization. The originality of the methodology consists in treating the case where the densities are depending on their own pressures without any major restriction neither on the permeability tensor nor on the mesh. Contrary to the ideas of [23], the point of the current scheme relies on a phase-by-phase sub-unpwinding approach so that we can recover the coercivity-like property. It allows on a second place for the preservation of the physical bounds on the discrete saturation. The convergence of the numerical scheme is therefore performed using classical compactness arguments. Numerical experiments are presented to exhibit the efficiency and illustrate the qualitative behavior of the implemented method. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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