  In the first paper of this series, we discussed analytically, in an
approximate way, the mixing processes which occur in slowly rotating stars when
the feed-back effects due to the diffusion-induced $\mu$-gradients are
introduced in the computations. We found that the classical scheme of
meridional circulation was dramatically modified, with important possible
consequences. Here we present a complete 2D numerical simulation of these
processes in a static stellar model. The helium microscopic diffusion and the
meridional advection are computed simultaneously, so that we can follow the
evolution of the abundances and mixing processes in the radiative zone. Most of
the effects discussed in paper I are confirmed. Some consequences will be
discussed in a forthcoming paper (Th\'eado and Vauclair 2002, paper III).
