An efficient solver for nearshore flows based on the WAF method

We describe an efficient and robust flow solver for the integration of the classic Nonlinear Shallow Water Equations (NSWE) on a beach of arbitrary topography. On the basis of the ‘shock capturing’ Weighted Average Flux (WAF) method, a numerical code is implemented which employs a space-splitting technique to integrate the NSWE over a horizontally two-dimensional domain (2DH). Special care is put in handling the moving shoreline and a new, efficient formulation of the shoreline boundary conditions is presented. This is based on the hydrodynamic equivalent of the cavitation condition used in gas dynamics. Model capabilities are illustrated by means of a number of tests (both 1DH and 2DH). These reveal that, though primarily conceived for modelling nearshore hydrodynamics, the solver can be successfully adopted even for studying the run-up of large tsunami waves.