基于二阶Godunov格式的SPH方法模拟弹塑性波的传播  

Simulation of elastic-plastic wave propagation based on smoothed particle hydrodynamics method with second order Godunov scheme

作　　者：郑晓梅[1] 徐志宏[1] 汤文辉[1] 冉宪文[1] 

机构地区：[1]国防科学技术大学理学院,长沙410073

出　　处：《振动与冲击》2011年第2期60-64,76,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(10802097;10672180)

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。A second-order Godunov-scheme SPH method was proposed to achieve higher accuracy and steeper representation of wave fronts than those calculated with first-order Godunov-scheme SPH method.The distribution of physical variables inside each particle was represented with a linear function using the proposed method.Therefore,the physical values at particle boundaries calculated through linear interpolation were used as the initial values of a Riemann problem between interacting particles.Riemann solvers and Taylor series were then introduced into the SPH method.One-dimensional problems of stress wave propagation were simulated with both first-order and second-order Godunov-scheme SPH methods.The results showed that the proposed method effectively improves the solution accuracy and is stable in both cases of tension and compression.

关 键 词：SPH Godunov格式 黎曼问题 TAYLOR展开 弹塑性应力波 

分 类 号：O242[理学—计算数学] O34[理学—数学]