A two-dimensional well-balanced numerical model for shallow water equations

作者：Amiri S M^*; Talebbeydokhti N; Baghlani A

来源：Scientia Iranica, 2013, 20(1): 97-107.

DOI：10.1016/j.scient.2012.12.001

• Flow discontinuities
• First-order centered scheme
• Runge-Kutta algorithm

Modeling flow discontinuities, due to a numerical approach, often pose severe challenges. In this way, a number of techniques like artificial viscosity (particularly for finite difference methods), shock fitting and etc. have been proposed. These techniques usually require ad-hoc terms which need to be adjusted through calibration. In this study, an efficient numerical model based on a shallow water equation is developed. The model uses a first-order centered (FORCE) scheme, in combination with the Surface Gradient Method, (SGM) for spatial discretization, and the third order Runge-Kutta algorithm for time integration. At first, it is demonstrated that the model is well-balanced, then, through several classical examples, such as a 1D dam-break on both dry and wet beds, transcritical flow over a bump, with and without shock, sub-critical flow over a bump, circular dam-break, small perturbation propagation, dam-break on a dry bed channel with varying widths and right-angled channel junctions, it is shown that the model is capable of capturing flow discontinuities. Furthermore, the model can simulate dry bed conditions, and also presents smooth symmetric results.

• 出版日期2013-2