EXPLICIT HIGHER ORDER SCHEMES FOR THE COUPLING OF DIMENSIONALLY HETEROGENEOUS FREE-SURFACE FLOW MODELS

The two-dimensional shallow water equations are widely used in the simulation of shallow free-surface flows. In some situations, even one-dimensional models may be accurate enough to capture the hydrodynamics of interest. In order to reduce overall numerical cost various methods for the numerical coupling of dimensionally heterogeneous models have been proposed in the literature. In this paper, we present a new Discontinuous Galerkin method of potentially arbitrary order for solving coupled 1d-2d shallow water equations based on an a-priori model decomposition. The accuracy of the method as well as its limitations are illustrated in a numerical experiment.