  We introduce a Rigid-Body Fluctuating Immersed Boundary (RB-FIB) method to
perform large-scale Brownian dynamics simulations of suspensions of rigid
particles in fully confined domains, without any need to explicitly construct
Green's functions or mobility operators. In the RB-FIB approach, discretized
fluctuating Stokes equations are solved with prescribed boundary conditions in
conjunction with a rigid-body immersed boundary method to discretize
arbitrarily-shaped colloidal particles with no-slip or active-slip prescribed
on their surface. We design a specialized Split--Euler--Maruyama temporal
integrator that uses a combination of random finite differences to capture the
stochastic drift appearing in the overdamped Langevin equation. The RB-FIB
method presented in this work only solves mobility problems in each time step
using a preconditioned iterative solver, and has a computational complexity
that scales linearly in the number of particles and fluid grid cells. We
demonstrate that the RB-FIB method correctly reproduces the Gibbs-Boltzmann
equilibrium distribution, and use the method to examine the time correlation
functions for two spheres tightly confined in a cuboid. We model a
quasi--two-dimensional colloidal crystal confined in a narrow microchannel and
hydrodynamically driven across a commensurate periodic substrate potential
mimicking the effect of a corrugated wall. We observe partial and full
depinning of the colloidal monolayer from the substrate potential above a
certain wall speed, consistent with a transition from static to kinetic
friction through propagating kink solitons. Unexpectedly, we find that
particles nearest the boundaries of the domain are the first to be displaced,
followed by particles in the middle of the domain.
