We extend a recently proposed mean-field hydrodynamics (MFH) discrete element simulation technique to consider the effects of a shear velocity profile on a model colloidal liquid containing monodisperse spherical particles in the non-newtonian shear thinning regime. The MFH method adapts Ermak＇s free draining brownian dynamics algorithm to include a local density approximation for the friction coefficient, semiempirically parametrized to reproduce the experimentally determined short-time diffusion coefficient. We have also generalized further the previous treatment to anew for a friction coefficient that is dependent on local density anisotropy. The behaviour of Ermak＇s equations of motion and also the ＇＇isotropic＇＇ and ＇＇anisotropic＇＇ MFH schemes with shear flow are compared. We show that, at equilibrium, the MFH approaches generate the same static averages as Ermak＇s method, and give good agreement with the Percus-Yevick prediction for hard-sphere structure factors using an r(-36) soft-sphere interaction. However, under shear, the three equations of motion give quite different rheological behaviour. The MFH methods produce higher viscosities, although the structures remain similar (e.g. all give a ＇＇string＇＇ phase) but at different shear rates. Variation in the specific details of the MFH equations of motion can promote or delay the development of long-range order with Peclet number.