二维溃坝问题的高分辨率数值模拟

High Resolution Numerical Simulations for Two Dimensional Dam Break Problems

对二维浅水方程空间方向的差分分裂，引入ＭＵＳＣＬ型的两参数限量函数，采用组合型的二阶ＴＶＤ格式，建立了浅水方程的高分辨率计算模型．以Ｆｒａｃｃｒｏｌｌｏ 等的部分溃坝实验模型为物理模型，模拟了该模型长历时的溃坝洪水演进过程，给出了典型位置的水位和速度计算并与其实验结果的比较．研究表明，在间断波附近，没有产生数值振荡，数值结果与实验数据相比除溃坝初期在口门附近的水位存在一定的差异外，其余位置和时刻吻合较好，特别是计算速度与实验测定值吻合更好．应用二维浅水方程和本文的高分辨率数值方法能有效地模拟溃坝波的演进过程．

A high resolution numerical scheme of the shallow water equations for solving dam break type problems was presented by applying a difference splitting approach in space and using a hybrid type of second order TVD scheme with the MUSCL type of two parameter limiter. Taking the experimental model of partial dam failure given by Fraccrollo et al. as the physical model, this paper simulated the long time routing courses for the dam break bores. Comparisons between the calculated water elevation and velocity and the experimental results at some representative sites were made. It shows there are no oscillatory phenomena near the discontinuities; and the calculated water elevations, especially the present velocity, agree well with the experimental results except near the dam site at the beginning of the dam failure. It further demonstrates that applying the two dimensional shallow water equation with the present high resolution scheme can effectively simulate the propagation of dam break bores, which may provide a scientific approach for the lucubration of other dam break flow characteristics and the decision making of the prevention of disasters.