二维溃坝绕流的WENO格式数值模拟

Two-Dimensional Dam-break Numerical Simulation Based on WENO Scheme

WENO(Weighted essentially non-oscillatory scheme)格式是一类新的高精度无振荡差分格式。本文将WENO格式和Runge-Kutta时间离散的思想应用于二维浅水方程组的求解,数值模拟矩形河道中大坝瞬间局部溃倒,下游有障碍物的洪水演进过程,并对模拟结果进行了分析,表明采用WENO格式所建立的高分辨率模型能够有效地模拟溃坝波的演进过程。

WENO is a new high-resolution and non-oscillatory differential scheme. With the WENO scheme and the Runge-Kutta time discertization method, the shallow water equations for numerical simulation of dam-break flows are deduced. The proposed mathematical model was used to predict 2D flood waves due to the partial instantaneous dam-break in a rectangular open channel with a rectangular cylinder barrier downstream, and the reliability of numerical results was analyzed. The comparison and the analysis show that the high-resolution model based on the WENO scheme becomes a good numerical model to effectively simulate the dam-break flows.