Shallow water flows over flooding areas by a flux-corrected finite element method

Abstract

In this work we construct a finite element method for shallow water flows with focus on problems with evolutionary coastlines. The method does not utilize ad hoc techniques to track the water-terrain interfaces and fulfills global conservation and positivity. The basis of the procedure is a generalized flux correction technique, and its application can be extended to diverse finite element solutions of the shallow water equations. Experiments are mainly concentrated on frictional flows with fronts propagating over dry regions.