On Numerical Stability of SPH Method in Solving 3D Elastic Solid Problems

摘要

The stability behavior of the Smoothed Particle Hydrodynamics (SPH) method in solving fluid issues and solid with flow features has been well investigated recently. In this paper, the stability characteristics of SPH method in simulating 3D elastic solid issues are thoroughly studied both theoretically and numerically. A stability criterion is proposed by conducting a 3D von Neumann stability analysis. The proposed formula is validated through systematic numerical tests. Factors such as particle distance, particle size, smoothing length of kernel function, Poisson ratio, shear modulus, non-uniform particle distribution are analyzed. The influence of artificial viscosity and velocity averaging upon numerical stability is discus Some meaningful conclusions are drawn, which can help understand and guarantee the numerical stability of the SPH method.