Physalis: A new O(N) method for the numerical simulation of particle flows

A new computational method for the full viscous flow past cylinders and spheres is described and illustrated with preliminary results. The starting point is the obvious remark that, due to the no-slip condition, in the body rest frame the velocity is very small near the body surface. Thus, in a small region around the body, the Stokes equations apply, which admit a closed-form analytic solution for both spheres and cylinders. These analytic solutions contain coefficients that are determined by matching with the outer flow by an iterative procedure. The operational count increases less than linearly with the number of bodies, which makes this method ideal for the direct numerical simulation of disperse particle flows at finite Reynolds numbers.