A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations

作者：Bollermann, Andreas; Chen, Guoxian; Kurganov, Alexander; Noelle, Sebastian^*

来源：Journal of Scientific Computing, 2013, 56(2): 267-290.

DOI：10.1007/s10915-012-9677-5

• Hyperbolic systems of conservation and balance laws
• Saint-Venant system of shallow water equations
• Finite volume methods
• Well-balanced schemes
• Positivity preserving schemes
• Wet/dry fronts

In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet-dry cells, which is presented in this paper for the one dimensional case. We realize the new reconstruction in the framework of the second-order semi-discrete central-upwind scheme from (Kurganov and Petrova, Commun. Math. Sci., 5(1):133-160, 2007). The positivity of the computed water height is ensured following (Bollermann et al., Commun. Comput. Phys., 10:371-404, 2011): The outgoing fluxes are limited in case of draining cells.

• 出版日期2013-8
• 单位RWTH Aachen; 武汉大学