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

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• 作者：A. Baeza^a ; ^{antonio.baeza@barcelonamedia.org} ; R. Donat^b ; ^donat@uv.es ; A. Martinez-Gavara^c ; ^gavara@uv.es
• 关键词：Hyperbolic systems ; Source terms ; Wet/dry front ; Shallow water equations
• 刊名：Applied Numerical Mathematics
• 出版年：2012
• 期刊代码：8_01689274
• 类别：cp
• 出版时间：April, 2012
• 卷：62
• 期：4
• 页码：264-277
• 文件大小：295 K

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 鈥榟omogeneous form鈥?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 鈥榟omogeneous form鈥? We also show that it maintains the well-balancing properties of the underlying hybrid schemes.