基于二阶Godunov格式的SPH方法模拟弹塑性波的传播

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (2) : 60-64.

论文

基于二阶Godunov格式的SPH方法模拟弹塑性波的传播

郑晓梅;徐志宏;汤文辉;冉宪文

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The Simulation of Elastic-Plastic Wave Propagation with Second-Order Godunov-scheme Smoothed Particle Hydrodynamics

ZHENG Xiao-mei; XU Zhi-hong;TANG Wen-hui;RAN Xian-wen

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摘要

针对一阶Godunov格式的SPH方法的计算精度和激波分辨率不高的问题，提出了二阶Godunov格式的SPH方法。新方法在求解相互作用的粒子间黎曼问题时，认为粒子内物理量呈线性分布，用线性插值后求得的值作为黎曼问题的初始值，然后把黎曼解和Taylor展开引入到SPH方法中。应用新方法对一维弹塑性应力波的传播进行了数值模拟，并与一阶Godunov格式的SPH方法进行比较.计算结果显示新方法有效地提高了计算精度和激波分辨率，同时验证了它的稳定性。

Abstract

A second-order Godunov-scheme SPH method is proposed to achieve higher accuracy and steeper representation of wave fronts than that calculated by first-order Godunov-scheme SPH method. The distribution of physical variables inside each particle is represented with linear functions in new method. Therefore physical values at particle boundaries which are calculated through linear interpolation are used as initial values of Riemann problem between interacting particles. Riemann solvers and Taylor series are then introduced into the SPH method. One-dimensional problems of stress wave propagation are simulated by both first-order and second-order Godunov-scheme SPH methods. The results show that the new method has effectively improved the solution accuracy and is stable both in tension and compression.

导出引用

郑晓梅;徐志宏;汤文辉;冉宪文. 基于二阶Godunov格式的SPH方法模拟弹塑性波的传播[J]. 振动与冲击, 2011, 30(2): 60-64

ZHENG Xiao-mei;XU Zhi-hong;TANG Wen-hui;RAN Xian-wen. The Simulation of Elastic-Plastic Wave Propagation with Second-Order Godunov-scheme Smoothed Particle Hydrodynamics[J]. Journal of Vibration and Shock, 2011, 30(2): 60-64