Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423252 | Applied Numerical Mathematics | 2012 | 14 Pages |
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.