In this article, we use the finite volume adaptive moving mesh method to solve the dam breaking problem and also the pollutant transport-diffusion problem. The choice of these problems is motivated by their nature, that is to say, problems of Riemann which are characterized by the fact that they are hyperbolic conservation laws with discontinuous solutions. The numerical solution of these types of problems by a numerical method using discretization of the domain such as the finite volume method is challenging. The main problem is to be able to approach these solutions appropriately in areas where they are discontinued. This task requires a very fine discretization step, leading to the use of a very high number of nodes for the solution. This is a major obstacle to the effectiveness of the method used. The technique of adaptive mesh method grid then intervenes to remedy this situation. The purpose of this article is to test the efficiency of the technique of adaptive mesh grid under the finite volume method.

simulation in shallow water of the free surface flow, Riemann problem, finite volume method, moving grids method.

Received: August 2, 2021; Revised: June 10, 2022; Accepted: July 16, 2022; Published: September 12, 2022

How to cite this article: Diakalia Koné, Kassiénou Lamien, Abdoulaye Samaké and Longin Somé, Numerical resolution of the dam break problem and the pollutant transport-diffusion problem by the moving grids method under the finite volume method, Far East Journal of Applied Mathematics 115 (2022), 1-24. http://dx.doi.org/10.17654/0972096022016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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