Analysis of miscible displacement through porous media with vanishing\n molecular diffusion and singular wells

2016/09/11 by Jérôme Droniou, Droniou, Jerome, Kyle S. Talbot +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.03244

openalex publication_date 2016/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article proves the existence of solutions to a model of incompressible\nmiscible displacement through a porous medium, with zero molecular diffusion\nand modelling wells by spatial measures. We obtain the solution by passing to\nthe limit on problems indexed by vanishing molecular diffusion coefficients.\nThe proof employs cutoff functions to excise the supports of the measures and\nthe discontinuities in the permeability tensor, thus enabling compensated\ncompactness arguments used by Y. Amirat and A. Ziani for the analysis of the\nproblem with L² wells [\Z. Anal. Anwendungen, 23(2):335--351, 2004].\nWe give a novel treatment of the diffusion-dispersion term, which requires\ndelicate use of the Aubin--Simon lemma to ensure the strong convergence of the\npressure gradient, owing to the troublesome lower-order terms introduced by the\nlocalisation procedure.\n

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