Abstract
In this paper we aim to do numerical simulation of the dimensionless coupled system (SW-LTDD) of Shallow Water equations (SWE) and Long term dynamic of sand dunes (LTDD) equation with a small parameter 𝜖, presented in our previous paper (Balde and Seck, Discrete Contin Dyn Syst Ser S 9(5):1521–1551, 2016) to model the erosion phenomenon. The small parameter 𝜖 was for the first time introduced in the paper Faye et al. (J Nonlinear Anal Appl 2016(2):82–105, 2016). In Balde and Seck (Discrete Contin Dyn Syst Ser S 9(5):1521–1551, 2016), we have proved existence and uniqueness of a solution of the coupled system. Now we give a numerical scheme of the system based on finite volume method. The stability of the scheme is proved and some numerical tests are performed.
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