Numerical analysis of a finite volume scheme for a seawater intrusion model with cross‐diffusion in an unconfined aquifer. Issue 3 (20th November 2017)

• Record Type: Journal Article
• Authors: Ait Hammou Oulhaj, Ahmed
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 3(2018)
• Page Start: 857
• Page End: 880
• Publication Date: 2017-11-20
• Subjects: convergence analysis -- cross‐diffusion -- entropy stability -- nonlinear discretization -- seawater intrusion -- unconfined aquifer -- Unsaturated porous media flow; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22234
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : 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.