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Article Dans Une Revue Foundations of Computational Mathematics Année : 2019

Unified convergence analysis of numerical schemes for a miscible displacement problem

Résumé

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the framework of the gradient discretisation method for diffusion operators on generic grids. We use it to establish a novel convergence result in L ∞ (0, T ; L 2 (Ω)) of the approximate concentration using minimal regularity assumptions on the solution to the continuous problem. The convection term in the concentration equation is discretised using a centred scheme. We present a variety of numerical tests from the literature, as well as a novel analytical test case. The performance of two schemes are compared on these tests; both are poor in the case of variable viscosity, small diffusion and medium to small time steps. We show that upstreaming is not a good option to recover stable and accurate solutions, and we propose a correction to recover stable and accurate schemes for all time steps and all ranges of diffusion.
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Dates et versions

hal-02492320 , version 1 (26-02-2020)

Identifiants

  • HAL Id : hal-02492320 , version 1

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Jérôme Droniou, Robert Eymard, Alain Prignet, Kyle S. Talbot. Unified convergence analysis of numerical schemes for a miscible displacement problem. Foundations of Computational Mathematics, 2019, 19 (2), pp.333-374. ⟨hal-02492320⟩
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