A new moving boundary shallow water wave equation numerical model

Abstract

A new moving boundary shallow water wave equation numerical model is presented. The model is adapted from the Selective Lumped Mass (SLM) numerical model. The wetting and drying scheme used is different to that in the SLM model. The SLM model is finite element in space, using fixed triangular elements, finite difference in time and is explicit. The numerical model has been tested against an analytical solution with good agreement between the numerical and analytical solutions. The numerical model proposed is useful for comparing against analytical moving boundary solutions. The analytical solution is presented for the first time, being for the case of frictionless one dimensional moving boundary nonlinear shallow water wave flow with cosine forcing in a bed with quadratically varying depth. The analytical solution, which is explicit, is useful for testing numerical models.