Numerical solution of the generalized Serre equations with the MacCormack finite-difference scheme

This paper describes a two‐dimensional numerical model to solve the generalized Serre equations. In order to solve the system equations, written in the conservative form, we use an explicit finite‐difference method based on the MacCormack time‐splitting scheme. The numerical method and the computational model are validated by comparing one‐ and two‐dimensional numerical solutions with theoretical and experimental results. Finally, the two‐dimensional model (in a horizontal plane) is tested in a domain with complicated boundary conditions.