一维溃坝洪水波的高精度数值模拟

One-dimensional dam-break numerical simulation based on ENO scheme

将ENO(Essentially Non-Oscillatory)格式和Runge-Kutta时间离散的思想应用于一维Saint-Venant方程组的求解,数值模拟溃坝洪水,得出了水位和流速的沿程分布。经与理论解比较可见,数值解在间断波附近没有出现数值振荡,水位和流速大小均符合较好,表明ENO格式是一类新的高精度无振荡差分格式,采用ENO格式所建立的高分辨率模型能够很好地模拟溃坝波的演进过程。

In this paper, the ENO scheme and the Runge-Kutta time discertization method were applied to the one-dimensional Saint-Venant water equations for numerical simulation of dam-break flows, and the water depth and the velocity along the distance were obtained. The computed results have no numerical oscillatory at the discontinuity. Comparisons of the computed results and analytical solutions are in agreement, which show that the ENO scheme is a new high-resolution and non-oscillatory differential scheme, and that the high-resolution model based on the ENO scheme can effectively simulate the dambreak flows.