A new particle shifting technique for SPH methods based on Voronoi diagram and volume compensation

Abstract

Particle shifting technique (PST) in smoothed particle hydrodynamics (SPH) is a useful strategy to render particle distribution isotropic for higher numerical accuracy and stability. However, the non-isotropic particle distribution near the free surfaces and volume non-conservation still often occur, which will degenerate accuracy in the long-time simulation with violent flows. In this study, the two major concerns are solved by proposing a new PST. The Voronoi cell is constructed for the particles with incomplete kernel support, and the difference between the Voronoi cell centroid and the corresponding particle location is used to determine the shifting vector, which ensures a very isotropic particle distribution and that no clustering or nonphysical gap occurs in these areas. For the free-surface particles, the shifting vector is determined according to the volume change and thus the volume conservation is ensured, where the volume is calculated conveniently with the merit of Voronoi diagram. The present method is compared with the other two advanced PST methods, and a set of challenging cases with violent flows is simulated to validate its superior properties in terms of maintaining isotropic particle distribution and volume conservation. Moreover, the efficiency of the present method is almost the same as those of other advanced PSTs. Overall, the new PST method presents a strong potential in the long-time simulation of violent flows in coastal engineering.