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The Physalis method is suitable for the simulation of flows with suspendedspherical particles. It differs from standard immersed boundary methods due tothe use of a local spectral representation of the solution in the neighborhoodof each particle, which is used to bridge the gap between the particle surfaceand the underlying fixed Cartesian grid. This analytic solution involvescoefficients which are determined by matching with the finite-differencesolution farther away from the particle. In the original implementation of themethod this step was executed by solving an over-determined linear system viathe singular-value decomposition. Here a more efficient method to achieve thesame end is described. The basic idea is to use scalar products of thefinite-difference solutions with spherical harmonic functions taken over aspherical surface concentric with the particle. The new approach is tested on anumber of examples and is found to posses a comparable accuracy to the originalone, but to be significantly faster and to require less memory. An unusual testcase that we describe demonstrates the accuracy with which the method conservesthe fluid angular momentum in the case of a rotating particle.

Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation