An SPH stress correction algorithm based on the quartic piecewise smooth kernel function

Abstract

<p indent="0mm">Smoothed particle hydrodynamics (SPH) is a popular adaptive Lagrangian mesh-free particle method. For the tensile instability problem in traditional SPH, according to the sufficient condition of tensile instability, a new quartic piecewise smooth kernel function with non-negative second derivative is proposed, and an SPH stress correction algorithm is obtained in this study. The numerical results show that the modified SPH algorithm can effectively describe the formation processes of 2D and 3D vdW liquid drops. Then, based on the modified SPH algorithm, the effects of different physical parameters on the particle distribution of 2D circular droplets are further discussed. The results show that, with the appropriate temperature or initial particle spacing, the boundary particles of circular droplets are neither clustered nor scattered, and as the fluid temperature or initial particle spacing increases, the boundary particles will be scattered. Conversely, the particle distribution of circular droplets becomes more uniform with the increase in the smooth length proportion coefficient.