用守恒元和解元法数值模拟二维溃坝洪水波

本文采用守恒元和解元方法（简称CE／SE法）来求解二维浅水方程，该方法从守恒积分型方程出发，严格遵守物理意义上的守恒律，通过设立守恒元和解元，从而提出一种新的数值模拟方法。用该方法计算得到的全溃的溃坝洪水波的数值解和理论解与文献中的实验值符合的较好。在此基础上，进一步对二维局部溃坝洪水波的演进过程进行模拟，结果表明，CE／SE法精度较高，稳定性较好，其溃坝洪水波的间断具有很高的分辨率，能很好的模拟溃坝洪水波的运动过程。

Numerical simulation of 2-D dam-break wave by using conservation element and solution element method

A new numerical scheme namely space-time Conservation Element/Solution Element (CE/SE) method is applied to solve the 2-D shallow water equations with space and time unified and treated on the same footing. By this method both local and global flux conservations in space and time are enforced. The computational results are in good consistence with both the analytic solutions and experimental results given by other authors. In addition, the evolution of 2-D dam break flood wave is also simulated with the CE/SE method. It shows that the CE/SE method is stable, high efficiency, high accuracy and high resolution for calculating the waves with discontinuity.