Development of SPH variable resolution using dynamic particle coalescing and splitting

In this paper a novel variable resolution method for SPH numerical scheme is presented. The key idea of the scheme is to dynamically modify the particle sizes by means of particle splitting and coalescing procedures. The SPH scheme adopted is variationally derived and this guaratees that both mass and momentum are conserved also in presence of particles with different smoothing lengths. To prevent highly anisotropic distributions of the particles, a generalized shifting procedure which can address also domains discretized with variable mass particles is included. The algorithm has been tested against Pouseuille flow showing the error introduced by the splitting and coalescing is negligible. The capability of the numerical scheme of increasing the efficiency is also showed: the Moving square in a box test case it has been shown that the particle refinement procedure is also able to increase the efficiency while maintaining the same level of accuracy, in comparison with uniform resolution simulations.