Particle transport velocity correction for the finite volume particle method for multi-resolution particle distributions and exact geometric boundaries

The finite volume particle method (FVPM) is a meshless computational fluid dynamics (CFD) method, where the fluid domain is represented by a set of overlapping particles, and boundaries are defined as exact geometries. Particle-based CFD methods, such as smoothed particle hydrodynamics (SPH) and FVPM, are susceptible to non-uniform particle distributions, which result in errors. Particle regularisation techniques, based on displacement or particle transport velocity, improve particle distributions. Here, improvements are made to the previous particle regularisation methods in SPH and FVPM. The method presented here takes advantage of the arbitrary Lagrangian-Eulerian nature of FVPM and applies a small correction to the particle transport velocity. It incorporates a novel symmetric formulation to maintain specified spatially varying resolution. Difficulties associated with the FVPM definition of the geometric boundaries are overcome, in that the correction method automatically adjusts to varying geometry segment size, without requiring fictitious boundary particles, as in SPH. The method is evaluated in a static multi-resolution test, cylinder in flow, and dambreak flow. Results show that the method yields improved particle distribution with few voids, with improved wall pressure results in the dambreak. The method maintains multi-resolution and adaptive particle distributions and is insensitive to the resolution of boundary geometry.