EFFECT OF PERTURBATION WAVELENGTH ON STABILITY OF ONE DIMENSIONAL STANDARD SPH
扰动波长对一维标准SPH稳定性的影响

The stability of one dimensional standard SPH with a cubic B-spline kernel is analyzed by von Neumann stability analysis method, and the effect of perturbation wavelength on the stability of SPH is discussed. The results of theoretical analysis are verified by numerical SPH computations of a one dimensional elastic bar, in which different wavelength perturbation are applied on the SPH particles. The numerical test indicates that the SPH stability is closely related with the perturbation wavelength. The numerical stable domain shape is the same as that of theoretical analysis except an offset of the stable domain boundaries of the numerical test. The SPH method used in this paper is the most unstable at the shortest perturbation wavelength, and it can be stable in tension at other perturbation wavelengths.