Author(s): Jingming Hou; Franz Simons; Qiuhua Liang; Reinhard Hinkelmann

Linked Author(s): jingming hou, franz simons, Reinhard Hinkelmann

Keywords: Finite volume method; hydrostatic reconstruction; shallow water equations; uneven bed; well-balanced scheme; wetting and drying

Abstract: Due to the universality, high efficiency and robustness, the hydrostatic non-negative water depth reconstruction method (HNRM) is attractive in solving the shallow water equations. However, the HNRM may lead to numerical failures when simulating dynamic shallow flows over uneven beds with large variations on coarse meshes. In order to mitigate this problem, an improved HNRM (IHNRM) is proposed in this work by introducing an energy head to better evaluate the slope source terms, which may be wrongly computed by the HNRM in such cases. Besides, the IHNRM is able to preserve the conservation property and the non-negative water depth as the HNRM. The good performance of the IHNRM is verified against three test cases involving thin flows and wetting and drying over uneven beds.

DOI: https://doi.org/10.1080/00221686.2013.858648

Year: 2014