Fast exact evaluation of particle interaction vectors in the finite volume particle method

摘要

The Finite Volume Particle Method (FVPM) is a mesh-free method which inherits many of the desirable properties of mesh-based finite volume methods. It relies on particle interaction vectors which are closely analogous to the intercell area vectors in the mesh-based finite volume method. To date, these vectors have been computed by numerical integration, which is not only a source of error but is also by far the most computationally expensive part of the algorithm. We show that by choosing an appropriate particle weight or kernel function, it is possible to evaluate the particle interaction vectors exactly and relatively quickly. The new formulation is validated for 2D viscous flow, and shown to enable modelling of free-surface flow.