A finite volume scheme for a seawater intrusion model with cross-diffusion

Ahmed Ait Hammou Oulhaj (1)

1 RAPSODI - Reliable numerical approximations of dissipative systems

We consider a finite volume scheme for a seawater intrusion model. It is based on a two-point flux approximation with upwind mobilities. The scheme preserves at the discrete level the main features of the continuous problem: the non-negativity of the solutions, the decay of the energy and the control of the entropy and its dissipation. Moreover the scheme converges towards a weak solution to the problem. Numerical results are provided to illustrate the behavior of the model and of the scheme.

Keywords: 65N08; decay of energy MSC (2010): 65M08; 35Q30; Finite Volume scheme; entropy stability

Domains: Analysis of PDEs [math.AP]; Numerical Analysis [math.NA]

Ahmed Ait Hammou Oulhaj. A finite volume scheme for a seawater intrusion model with cross-diffusion. FVCA8 2017 - International Conference on Finite Volumes for Complex Applications 8, Jun 2017, Lille, France. pp.421-429, ⟨10.1007/978-3-319-57397-7_35⟩. ⟨hal-01541229⟩