  We propose a numerical method to simulate electrohydrodynamic phenomena in
charged colloidal dispersions. This method enables us to compute the time
evolutions of colloidal particles, ions, and host fluids simultaneously by
solving Newton, advection-diffusion, and Navier--Stokes equations so that the
electrohydrodynamic couplings can be fully taken into account. The
electrophoretic mobilities of charged spherical particles are calculated in
several situations. The comparisons with approximation theories show
quantitative agreements for dilute dispersions without any empirical
parameters, however, our simulation predicts notable deviations in the case of
dense dispersions.
