  We describe a method to simulate the dynamics of charged colloidal particles
suspended in a liquid containing dissociated ions and salt ions. Regimes of
prime current interest are those of large volume fraction of colloids, highly
charged particles and low salt concentrations. A description which is tractable
under these conditions is obtained by treating the small dissociated and salt
ions as continuous fields, while keeping the colloidal macroions as discrete
particles. For each spatial configuration of the macroions, the electrostatic
potential arising from all charges in the system is determined by solving the
nonlinear Poisson--Boltzmann equation. From the electrostatic potential, the
forces acting on the macroions are calculated and used in a Brownian dynamics
simulation to obtain the motion of the latter. The method is validated by
comparison to known results in a parameter regime where the effective
interaction between the macroions is of a pairwise Yukawa form.
