  Brownian dynamics algorithms integrate numerically Langevin equations and
allow to probe long time scales in simulations. A common requirement for such
algorithms is that interactions in the system should vary little during an
integration time step: therefore, computational efficiency worsens as the
interactions become steeper. In the extreme case of hard-body interactions,
standard numerical integrators become ill defined. Several approximate schemes
have been invented to handle such cases with little emphasis on testing the
correctness of the integration scheme. Starting from the two-body Smoluchowsky
equation, we discuss a general method for the overdamped Brownian dynamics of
hard-spheres, recently developed by one of us. We test the accuracy of the
algorithm with the exact solution of the Smoluchowsky equation in the case of
twobody collisions and in the low-density limit.
