Physalis: A new (o)(N) method for the numerical simulation of disperse systems: Potential flow of spheres

This paper presents a new approach to the direct numerical simulation of po tential problems with many spherical infernal boundaries, e.g., many sphere s in potential flow. The basic idea is to use a local analytic representati on valid near the particle and to match it to an external field calculated by a standard finite-difference (or finite-element) method. In this way the geometric complexity arising from the irregular relation between the parti cle boundary and the underlying mesh is avoided and fast solvers can be use d. The results suggest that the computational effort increases less than pr oportionally to the number of particles and, additionally, that meshes that would be excessively coarse as measured in terms of particle radius in a c onventional calculation can be used without significant loss of accuracy In separate (if preliminary) work the same approach has been extended to the simulation of viscous flow about spheres and cylinders at finite Reynolds n umbers. (C) 2001 Academic Press.