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We introduce methods for large scale Brownian Dynamics (BD) simulation ofmany rigid particles of arbitrary shape suspended in a fluctuating fluid. Ourmethod adds Brownian motion to the rigid multiblob method at a cost comparableto the cost of deterministic simulations. We demonstrate that we canefficiently generate deterministic and random displacements for many particlesusing preconditioned Krylov iterative methods, if kernel methods to efficientlycompute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and it"square" root are available for the given boundary conditions. We address amajor challenge in large-scale BD simulations, capturing the stochastic driftterm that arises because of the configuration-dependent mobility. Unlike thewidely-used Fixman midpoint scheme, our methods utilize random finitedifferences and do not require the solution of resistance problems or thecomputation of the action of the inverse square root of the RPY mobilitymatrix. We construct two temporal schemes which are viable for large scalesimulations, an Euler-Maruyama traction scheme and a Trapezoidal Slip scheme,which minimize the number of mobility solves per time step while capturing therequired stochastic drift terms. We validate and compare these schemesnumerically by modeling suspensions of boomerang shaped particles sedimentednear a bottom wall. Using the trapezoidal scheme, we investigate thesteady-state active motion in a dense suspensions of confined microrollers,whose height above the wall is set by a combination of thermal noise and activeflows. We find the existence of two populations of active particles, slowerones closer to the bottom and faster ones above them, and demonstrate that ourmethod provides quantitative accuracy even with relatively coarse resolutionsof the particle geometry.

Large Scale Brownian Dynamics of Confined Suspensions of Rigid Particles