基于二阶Godunov格式的SPH方法模拟弹塑性波的传播

摘要

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.Onedimensional 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.%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.