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Numerical analysis of a finite volume scheme for a seawater intrusion model with cross‐diffusion in an unconfined aquifer
Author(s) -
Ait Hammou Oulhaj Ahmed
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22234
Subject(s) - finite volume method , dissipation , nonlinear system , numerical diffusion , context (archaeology) , mathematics , control volume , mechanics , upwind scheme , mathematical analysis , geology , physics , thermodynamics , paleontology , quantum mechanics , discretization
We consider a degenerate parabolic system modeling the flow of fresh and saltwater in a porous medium in the context of seawater intrusion. We propose and analyze a finite volume scheme based on two‐point flux approximation with upwind mobilities. The scheme preserves at the discrete level the main features of the continuous problem, namely the nonnegativity of the solutions, the decay of the energy and the control of the entropy and its dissipation. Based on these nonlinear stability results, we show that the scheme converges toward a weak solution to the problem. Numerical results are provided to illustrate the behavior of the model and of the scheme.