Particle transport velocity correction for complex boundaries in the Finite Volume Particle Method

Particle methods such as smoothed particle hydrodynamics (SPH) and the finite volume particle method (FVPM) can suffer from strongly non-uniform and anisotropic particle distributions when purely Lagrangian particle motion is employed, resulting in numerical error. In this paper, we evaluate two Arbitrary Lagrangian Eulerian (ALE) particle transport velocity corrections for FVPM, adapted from SPH methods with a new treatment for boundaries without fictitious particles. The methods are tested on Taylor-Green flow, lid driven cavity flow (with additional complex geometry), oscillating free-surface flow, and dam-break free-surface flow. Results show that the correction formulation can maintain good particle distribution with nearly Lagrangian particle motion. The new boundary treatment is found to be effective for varying spatial resolution and complex geometry over a range of scales, without fictitious boundary particles and without parameter tuning.