The viscoelastic properties of model stable colloidal dispersions are
calculated using Brownian dynamics simulations with a free-draining mo
del for the hydrodynamic interactions. In this report we describe a nu
mber of alternative routes to the dynamic moduli, making a comparison
of the relative merits of the approaches. These include the use of the
Green-Kubo formulas (used widely by the molecular simulation communit
y but little used so far in colloid modeling), which gives the linear
stress relaxation function from stress fluctuations in an unsheared mo
del colloidal liquid. We also consider the direct application of an os
cillating shear strain, as used in experiment, changing the frequency
and strain amplitude in discrete jumps. This method is developed to co
nsider a continuously varying sweep through frequency (constant strain
amplitude) or strain amplitude (constant frequency). This route avoid
s problems associated with equilibration at each frequency. We avoid e
rrors associated with truncation of the Fourier transform by cutting i
t off smoothly with a broad Gaussian. We concentrate on the real and i
maginary parts of the complex storage modulus G, the storage modulus
G', and loss modulus G'', being the most frequently cited viscoelastic
functions. For very large amplitudes, we find oscillatory-shear-induc
ed crystallization to a fcc structure.