A reappraisal of Taylor–Galerkin algorithm for drying–wetting areas in shallow water computations

Non‐linear shallow water equations are a useful approximation to phenomena such as estuary dynamics, tidal propagation, breaking of a dam, flood waves, etc. Quite frequently they involve propagation over dry beds and drying of wet zones, for which boundary changes. To solve this problem either special techniques such as remeshing and Arbitrary Lagrangian Eulerian formulations or algorithms initially developed for flows exhibiting shocks have been proposed in past years. The purpose of this paper is to show how classical finite elements formulations, such as Taylor–Galerkin can be applied to solve the problem to wetting–drying areas in a simple yet efficient manner.