基于简单WENO-RKDG的溃坝问题数值模拟  

Numerical simulation of two-dimensional dam-break flow based on the simple WENO Limiter-Runge-Kutta discontinuous Galerkin method

作　　者：吴泽艳[1] 杨忠勇[1] 

机构地区：[1]三峡大学水利与环境学院,宜昌443002

出　　处：《应用力学学报》2017年第6期1126-1133,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(41506103);三峡大学人才科研启动基金(KJ2014B031);水电工程水文气象重大关键技术应用研究(DJ-ZDZX-2016-02-06)

摘　　要：对溃坝问题水流间断面的高精度、高分辨率数值模拟是水动力学的重要内容。简单加权本质无振荡(WENO)限制器由"问题单元"及其相邻单元的解重构"问题单元"的解,从而抑制数值解的非物理振荡,能够很好地模拟间断问题。本文详细介绍了简单WENO限制器的基本原理和过程。将简单WENO限制器-Runge-Kutta间断Galerkin方法应用于二维浅水控制方程的求解中,对二维矩形明渠中大坝瞬间全溃、局部溃塌所致的水流运动进行了数值模拟,并将数值计算结果与理论分析进行了比较。计算结果表明,方法能够清晰地捕捉到溃坝全过程中的间断,没有非物理的振荡现象发生,简单WENO限制器-RKDG方法能够很好地模拟溃坝波的演进过程。High order accurate and high resolution numerical simulation for dam-break problems is an important part of hydraulics. The simple weighted essentially non-oscillatory(WENO) limiter has a strong adaptability to suppress non-physical oscillations by reconstructing the polynomial on 'trouble element' and its neighboring cells. In this paper, the simple WENO limiter is introduced and the simple WENO limiter-Runge-Kutta discontinuous Galerkin method is applied to solve the equations of shallow 2-D dam-break flow. The process of flood wave propagation due to the instantaneous complete and local dam-break in the 2-D rectangular open channel is simulated. Calculations suggest that the method can clearly capture the discontinuity in the whole process of dam-break, and no nonphysical oscillation phenomena appear. The validity of the method is verified by the comparison of the calculated result with the theoretical analysis, which shows that the simple WENO Limiter-Runge-Kutta discontinuous Galerkin method is feasible to simulate the process of flood wave propagation due to the instantaneous dam-break.

关 键 词：溃坝 浅水波方程 Runge-Kutta间断Galerkin法 简单WENO限制器 数值模拟 

分 类 号：TV131.4[水利工程—水力学及河流动力学] O241.82[理学—计算数学]