Moving Boundary Problems in the Finite Volume Particle Method

The Finite Volume Particle Method (FVPM) is a mesh-free method for fluid dynamics. The method is formulated from the integral form of the conservation equations, and particle interactions are described in terms of inter-particle fluxes. Boundaries can be implemented without the need for fictitious particles, and the method is conservative. The motion of the particles can be independent of the fluid velocity. The advantages of Lagrangian particle motion are numerous, allowing free-surface and moving boundary problems to be simulated with relative ease. However, Lagrangian particle motion in FVPM has been problematic due to the development of highly non-uniform particle distributions, which affect the accuracy and robustness of the method. In this article, a particle velocity correction is proposed which acts to maintain the uniformity of the moving particle cloud, regardless of the flow configuration. This is facilitated by FVPM due to the independence of particle and fluid velocities, in a similar manner to Arbitrary Lagrangian-Eulerian methods for mesh-based discretisations. The scheme is assessed for incompressible lid-cavity flow at Reynolds number 1000 (SPHERIC benchmark 3). In addition, the suitability of the method for moving boundary problems is demonstrated for incompressible flow over a moving square cylinder in a fixed rectangular walled enclosure (SPHERIC benchmark 6).