浅水流动的模拟方法比较

Comparison of different schemes for shallow water flow

本文研究浅水模拟中几种具有代表性的计算格式,包括不同阶数的简单格式、迎风格式、利用不同通量控制器的TVD格式以及基于分子运动理论的KFVS格式。通过对具有多种不同水流以及间断的一维溃坝的模拟,这些格式的优劣从各种典型数值现象中体现出来。最后用筛选后的格式对一维溃坝物理实验以及二维扩展渠道水流进行模拟。由于KFVS格式符合基本的流体分子运动规律,虽然引入了一定的耗散误差,但此格式无论对一维问题还是二维问题总体模拟效果都较佳。

In this paper, eight typical scheme is listed, including first-order and second-order naive scheme, upwind scheme, TVD scheme with different slope limiter and scheme based on kinetic theory. In numerical experiments on the one-dimensional dam-break problem, which admits various types of flows, numerical results are compared with theoretical solutions and experiment results. Advantages and disadvantages of these schemes are given.