Implicit moving finite element model of the 2D shallow-water equations

This paper describes a method for determining implicitly, the waterline and flow variables in shallow water. In particular, the shallow-water equations are applied to open channels with sloping sidewalls and dam-break flow over initially dry beds. The domain limits are time dependent in both cases, but only the former has a steady state. Arbitrary Lagrangian-Eulerian descriptions of the two-dimensional shallow-water equations are used to describe the time-dependent waterline formed by the water-surface/channel-bed intersection. The model uses an implicit Petrov-Galerkin moving-finite-element representation of the shallow-water equations. Simultaneous solutions of the two-dimensional shallow-water equations and waterlines are obtained. The implicit approach relaxes time-step size limitations and the Petrov-Galerkin test function provides numerical stability for advection-dominated flows. The model offers a viable means of representing shadow-water flows where the boundary locations are not known a priori.