In this article, we have targeted the computation of an efficient numerical solution of a Richard problem using a family of methods constructed by Mackenzie [14] following the principle of the finite volume method that can use a moving grid. As part of an evaluation of this solution, a control problem with analytical solution, that of Burgers was also solved by the same approach. The direct application of the considered method was confronted with severe oscillations of the numerical solution of Richard’s problem, which was however not the case for the solution of Burgers’ problem. An increase in the number of grid points did not eliminate these oscillations. To see them disappear, it was necessary to resort to the use of flux limiters in the numerical scheme. These different results are supported by graphical representations presented in this paper.

moving grid, iterative finite volume method, Eulerian form, Lagrangian form, flux limiter.

Received: November 16, 2022; Accepted: January 5, 2023; Published: January 12, 2023

How to cite this article: Kassiénou LAMIEN, Mamadou OUÉDRAOGO, Moumini KERE, Bisso SALEY and Longin SOMÉ, Experimentation of a family of iterative finite volume methods with moving grid to solve a Richard’s problem, Advances and Applications in Discrete Mathematics 37 (2023), 1-20. http://dx.doi.org/10.17654/0974165823008

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

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