Accelerated Stokesian dynamics: Brownian Motion

BANCHIO, A. J.; BRADY, J. F.

JOURNAL OF CHEMICAL PHYSICS

Año: 2003 vol. 118 p. 10323 - 10323

0021-9606

A new Stokesian dynamics (SD) algorithm for Brownian suspensions is presented. Theimplementation is based on the recently developed accelerated Stokesian dynamics (ASD)simulation method [Sierou and Brady, J. Fluid Mech. 448, 115 (2001)] for non-Brownian particles.As in ASD, the many-body long-range hydrodynamic interactions are computed using fast Fouriertransforms, and the resistance matrix is inverted iteratively, in order to keep the computational costO(N log N). A fast method for computing the Brownian forces acting on the particles is applied bysplitting them into near- and far-field contributions to avoid the O(N^3) computation of the squareroot of the full resistance matrix. For the near-field part, representing the forces as a sum of pairwisecontributions reduces the cost to O(N); and for the far-field part, a Chebyshev polynomialapproximation for the inverse of the square root of the mobility matrix results in an O(N^1.25 log N)computational cost. The overall scaling of the method is thus roughly of O(N^1.25 log N) and makespossible the simulation of large systems, which are necessary for studying long-time dynamicalproperties and/or polydispersity effects in colloidal dispersions. In this work the method is appliedto study the rheology of concentrated colloidal suspensions, and results are compared withconventional SD. Also, a faster approximate method is presented and its accuracy discussed.