Particle packing algorithm for SPH schemes

AbstractUsing some intrinsic features of the Smoothed Particle Hydrodynamics schemes(SPH), an innovative algorithm for the initialization of the particle distribution hasbeen defined. The proposed particle packing algorithm allows a drastic reductionof the numerical noise due to particle resettlement during the early stages of theflow evolution. Moreover, thanks to its structure, it can be easily derived startingfrom whatever SPH scheme and applies under the hypotheses that the fluid isweakly-compressible or incompressible as well. A broad range of numerical testcases proved this tool to be fast, robust and reliable also for complex geometricalconfigurations.Key words: Meshless methods, Smoothed Particle Hydrodynamics, Particleinitialization, Lagrangian Systems.IntroductionIn the Smoothed Particle Hydrodynamics scheme (SPH) the matter of howinitialize the particle positions plays a relevant role. If particles are not initiallyset in “equilibrium” positions, they may resettle giving rise to spurious motionswhich can strongly a ect the fluid evolution.Here, the acceptation of the word “equilibrium” deserves a clarification.We refer to an equilibrium configuration as the set of particle positions which,under static conditions, does not lead to particle resettlement. As proved in thefollowing, the spurious particle motion is caused by inaccuracies in the SPHrepresentation of the pressure gradient. Specifically, these inaccuracies largelyincrease when the particle distribution is anisotropic and disordered. At worst, the