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.