Abstract
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 nonnegativity 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.
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Oulhaj, A.A.H.: Numerical analysis of a finite volume scheme for a seawater intrusion model with cross-diffusion in an unconfined aquifer (2017). HAL: hal-01432197, submitted
Acknowledgements
The author thanks the team Inria/Rapsodi, the Labex CEMPI (ANR-11-LABX-0007-01) and the project GEOPOR (ANR-13-JS01-0007-01) for their support.
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Oulhaj, A.A.H. (2017). A Finite Volume Scheme for a Seawater Intrusion Model with Cross-Diffusion. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_35
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DOI: https://doi.org/10.1007/978-3-319-57397-7_35
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