基于简单WENO-RKDG的溃坝问题数值模拟

发布时间：2018-05-18 08:27

本文选题：溃坝 + 浅水波方程　；参考：《应用力学学报》2017年06期

【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。
[Abstract]:The high precision and high resolution numerical simulation of water flow discontinuity is an important part of hydrodynamics. The simple weighted essential non-oscillation (WENOO) limiter reconstructs the solution of the "problem unit" from the solution of the "problem unit" and its adjacent elements, thus suppressing the non-physical oscillation of the numerical solution, and can well simulate the discontinuous problem. This paper introduces the basic principle and process of simple WENO limiter in detail. The simple WENO limiter Runge-Kutta discontinuous Galerkin method is applied to the solution of 2-D shallow water governing equation. The flow motion caused by the instantaneous total collapse and local collapse of a dam in a two-dimensional rectangular open channel is numerically simulated. The numerical results are compared with the theoretical analysis. The results show that the method can clearly capture the discontinuity in the whole process of dam break and there is no non-physical oscillation. The simple WENO limiter RKDG method can well simulate the evolution process of dam-break wave.
【作者单位】：三峡大学水利与环境学院;
【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)
【分类号】：TV122.4;TV131.2

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