Abstract

We present a stable finite element formulation for the shallow water equations using the finite increment calculus (FIC) procedure. This research is focused on the stability properties of the FIC technique and uses linear triangles for the spatial discretization with an equal order of interpolation for all the variables. The extension to higher order polynomial interpolation functions and different geometries is straightforward. The present FIC-FEM procedure is also able to introduce artificial viscosity for an adequate shock capturing. An implicit time integration has been used. Special attention has been payed to the dry domain in order to solve the moving boundaries with a fixed mesh Eulerian approach. Three academic examples are included in order to test the capabilities of the FIC-FEM procedure: the global stabilization, the shock capturing technique and the dry-wet interface. An experimental benchmark tests the overall accuracy of the present formulation.