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Brownian Dynamics of Active Sphere Suspensions Confined Near a No-Slip Boundary

We develop numerical methods for performing efficient Brownian dynamics of colloidal suspensions confined to remain in the vicinity of a no-slip wall by gravity or active flows. We present a stochastic Adams-Bashforth integrator for the Brownian dynamic equations, which is second-order accurate deterministically and uses a random finite difference to capture the stochastic drift proportional to the divergence of the mobility matrix. We generate the Brownian increments using a Krylov method, and show that for this geometry the number of iterations is independent of the number of particles. This allows us to develop an implementation on Graphical Processing Units (GPUs) that can efficiently simulate many thousands of particles over relevant timescales. We demonstrate the utility of our methods by simulating a recently-observed fingering instability in an active suspension of colloidal rollers. Our numerical experiments show that the thermal fluctuations are critical to set the characteristic height of the colloids above the wall, which in turn controls the growth rate of the fingering instability.