Accelerated Stokesian Dynamics simulations

A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations g overning the motion of N particles suspended in a viscous fluid at low part icle Reynolds number are solved accurately and efficiently, including all h ydrodynamic interactions, but with a significantly lower computational cost of O(N In N). The main differences from the conventional SD method lie in the calculation of the many-body long-range interactions, where the Ewald-s ummed wave-space contribution is calculated as a Fourier transform sum and in the iterative inversion of the now sparse resistance matrix. The new met hod is applied to problems in the rheology of both structured and random su spensions, and accurate results are obtained with much larger numbers of pa rticles. With access to larger N, the high-frequency dynamic viscosities an d short-time self-diffusivities of random suspensions for volume fractions above the freezing point are now studied. The ASD method opens up an entire new class of suspension problems that can be investigated, including parti cles of non-spherical shape and a distribution of sizes, and the method can readily be extended to other low-Reynolds-number-flow problems.