Modelling wetting and drying effects over complex topography

作者：G. W. Tchamen, R. Kahawita · 发表于：Hydrological Processes · 年份：1998 · DOI：10.1002/(sici)1099-1085(19980630)12:8<1151::aid-hyp676>3.0.co;2-y · 被引用次数：32 · 研究领域：Computational Fluid Dynamics and Aerodynamics、Advanced Numerical Methods in Computational Mathematics、Navier-Stokes equation solutions

The numerical simulation of free surface flows that alternately flood and dry out over complex topography is a formidable task. The model equation set generally used for this purpose is the two-dimensional (2D) shallow water wave model (SWWM). Simplified forms of this system such as the zero inertia model (ZIM) can accommodate specific situations like slowly evolving floods over gentle slopes. Classical numerical techniques, such as finite differences (FD) and finite elements (FE), have been used for their integration over the last 20–30 years. Most of these schemes experience some kind of instability and usually fail when some particular domain under specific flow conditions is treated. The numerical instability generally manifests itself in the form of an unphysical negative depth that subsequently causes a run-time error at the computation of the celerity and/or the friction slope. The origins of this behaviour are diverse and may be generally attributed to: 1. The use of a scheme that is inappropriate for such complex flow conditions (mixed regimes). 2. Improper treatment of a friction source term or a large local curvature in topography. 3. Mishandling of a cell that is partially wet/dry. In this paper, a tentative attempt has been made to gain a better understanding of the genesis of the instabilities, their implications and the limits to the proposed solutions. Frequently, the enforcement of robustness is made at the expense of accuracy. The need for a positive scheme,...