A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations

In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet-dry cells, which is presented in this paper for the one dimensional case. We realize the new reconstruction in the framework of the second-order semi-discrete central-upwind scheme from (Kurganov and Petrova, Commun. Math. Sci., 5(1):133-160, 2007). The positivity of the computed water height is ensured following (Bollermann et al., Commun. Comput. Phys., 10:371-404, 2011): The outgoing fluxes are limited in case of draining cells.