A corrected smooth particle hydrodynamics formulation of the shallow-water equations

A shallow-waters formulation based on a variable smoothing length SPH method is presented. This new formulation of the SPH equations treats the continuum as a Hamiltonian system of particles where the constitutive relationships for the materials are introduced via an internal energy term. Some of the advantages of the new SPH formulation are evident in the solution of the shallow-water equations for expanding flows. The shallow-waters approach incorporates the terrain into the equation of motion through terrain properties evaluated using SPH methodology. Several examples are presented on the simulation of breaking dams on different geometries. A comparison with the analytical solutions is also included.