This article describes a discontinuous implementation of residual distribution for shallow-water flows. The emphasis is put on the space-time implementation of residual distribution for the time-dependent system of equations with discontinuity in time only. This lifts the timestep restriction that even implicit continuous residual distribution schemes invariably suffer from, and thus leads to a...

We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary schem...

Even with current extreme scale systems, the accurate simulation of tsunamis continues to be a challenging problem. One commonly used model for this task are the hydrostatic shallow water equations which, however, are not able to represent all relevant physical effects of tsunamis. In this paper, we therefore show how to solve the non-hydrostatic shallow water equations in parallel within the p...