| Autor: |
Mostefai Mohamed Lamine, Choucha Abdelbaki, Cherif Bahri |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
Demonstratio Mathematica, Vol 54, Iss 1, Pp 510-526 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2391-4661 |
| DOI: |
10.1515/dema-2021-0036 |
| Popis: |
In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞{L}^{\infty } stability under appropriate CFL conditions and BV{\rm{BV}} estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1{L}^{1}. Results of numerical experiments are presented to validate the theoretical analysis. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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