Accelerated Stokesian Dynamics simulations
A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the many-body long-range interactions, where the Ewald-summed wave-space contribution is calculated as a Fourier transform sum and in the iterative inversion of the now sparse resistance matrix. The new method is applied to problems in the rheology of both structured and random suspensions, and accurate results are obtained with much larger numbers of particles. With access to larger N, the high-frequency dynamic viscosities and 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 particles of non-spherical shape and a distribution of sizes, and the method can readily be extended to other low-Reynolds-number-flow problems.
"Reprinted with the permission of Cambridge University Press." (Received January 5 2001) (Revised April 26 2001) Published online 26 November 2001 This work was supported in part by grants NAG3-2166 and NAG8-1661 from NASA. The authors benefited greatly from discussions with Professor J. J. L. Higdon on the PME method for Stokes flow. An anonymous referee is thanked for the suggestion of the random forces to determine the short-time self-diffusivity.