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

Author:
A. Baeza   R. Donat   A. Martinez-Gavara  


Journal:
Applied Numerical Mathematics


Issue Date:
2012


Abstract(summary):

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. [All rights reserved Elsevier].


Page:
264-277


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