A split‐characteristic based finite element model for the shallow water equations

Abstract

Abstract A new algorithm for the solution of the shallow water equations is introduced. The formulation is founded on a suitable operator‐splitting procedure for which a characteristic‐based rational form of including balancing dissipation terms is achieved. In the semi‐explicit form the method circumvents the requirement of a critical time step given in terms of the wave celerity, which is restrictive for the analysis of long‐wave propagation in shallow waters. In this work the robustness of the algorithm is illustrated for transient shallow water problems and for some supercritical flows, where the choice of an algorithm with optimal diffusion properties is manifest.