On Particle Shifting Techniques (PSTs): Analysis of existing laws and proposition of a convergent and multi-invariant law

This paper addresses the Particle Shifting Technique (PST) in the SPH schemes. Improving the accuracy of SPH schemes leads to particle clustering along the flow streamlines which turns to be detrimental for the simulations. PSTs aim at avoiding this adverse effect by slightly disordering the particles, allowing to retrieve a regular particle distribution within the kernel interpolation support. The gain in accuracy is such that this technique is now commonly adopted by the SPH practitioners, however the conditions that should be respected by a PST are not clearly discussed in the literature. In this paper, such conditions are exposed and their fulfillment by the main existing PSTs of the literature is analyzed. None of these existing PSTs fully satisfying these conditions, a novel PST is introduced. The proposed PST is validated for three different SPH schemes on 2D and 3D test cases, in presence of free-surface and solid boundaries.