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

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.

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