A new second-order modified hydrostatic reconstruction for the shallow water flows with a discontinuous topography

Abstract

We consider a new second-order hydrostatic reconstruction (HR) based on the bottom topography, the depth-averaged velocity, and the water surface level for the shallow water flows with discontinuous bottom topography. The Audusse's second-order hydrostatic reconstruction (HR) (Audusse et al. (2004) [1]) fails to correctly reflect the wave pattern for the large discontinuous bottom topography. We propose a new modified HR method to overcome this numerical difficulty. The well-balancing property is obtained by using the information of the neighboring cells which is used to modify the reconstruction at the wet-dry front. The positivity preserving property is ensured by a “draining” time-step technique. A number of classical problems are successfully solved by the new scheme. Especially, the new scheme yields superior results for the shallow downhill flow over steps.