A numerical treatment of wet/dry zones in well-balanced hybrid schemes for shallow water flow

摘要

The flux-limiting technology that leads to hybrid, high resolution shock capturing schemes for homogeneous conservation laws has been successfully adapted to the non-homogeneous case by the second and third authors. In dealing with balance laws, a key issue is that of well-balancing, which can be achieved in a rather systematic way by considering the 'homogeneous form' of the balance law. The application of these techniques to the shallow water system requires also an appropriate numerical treatment for the wetting/drying interfaces that appear initially or as a result of the flow evolution. In this paper we propose a numerical treatment for wet/dry interfaces that is specifically designed for schemes based on the "homogeneous form'. We also show that it maintains the well-balancing properties of the underlying hybrid schemes.