一种可考虑界面不连续的改进SPH方法

SPH方法模拟工程问题时通常遇到不连续的物理量,因此有必要引入不连续的SPH方法.本文基于Taylor展开公式推导了2D和3D的不连续SPH公式.针对越过材料界面不连续物理量的计算,给出了大变形计算中确定不连续位置的方法,基于Taylor展开公式,从理论上给出了确定不连续公式中x_(k)点的方法,并用数值方法验证了此方法的有效性.比较和讨论了初始SPH方法,CSPM方法与不连续SPH方法处理不连续量的效果.结果显示不连续SPH方法在计算不连续量时有较大的优势.

An improved SPH method in the discontinuous interface problem

It is necessary to introduce the discontinuous SPH method because discontinuous physical quantities often appear in SPH numerical simulations. Based on Taylor series expansion, discontinuous SPH expressions in 2D and 3D simulations were derived. For the computation of discontinuous physical quantities at material interface with large deformations, how to determine discontinuous locations was presented, and the method to determine x_k in discontinuous formulas was proposed theoretically based on Taylor series expansion and validated numerically. Initial SPH method, CSPM method and the discontinuous SPH method were compared and discussed when simulating discontinuous quantities. The results show that the discontinuous SPH method is more attractive when simulating discontinuous quantities.