A shallow water model for the propagation and breaking of surface waves is proposed in the form of a hyperbolic system of conservation laws, with dispersive effects introduced through a relaxation term and a localized dissipative term. The latter is activated in regions where a new breaking criterion is satisfied. The objective is to obtain a simple mathematical and numerical structure while capturing the main features of wave breaking. The governing equations, the associated breaking criterion, and the numerical strategy used for their approximation are presented. Particular attention is paid to the persistence of the dissipation once activated, and to its influence on the behaviour of solutions. Several test cases illustrate the properties of the model.
By Matthew Juniper
By Sergey Gavrilyuk
By David Lannes
