In simulations of phase separation kinetics, large length and time scales are involved due to the mesoscopic size of the polymer coils, and the structure formation on still larger scales of length and time. We apply a coarse-grained model of hexadecane dissolved in supercritical carbon dioxide, for which in previous work the equilibrium phase behavior has been established by Monte Carlo methods. Using parallelized simulations on a multiprocessor supercomputer, large scale molecular dynamics simulations of phase separation following pressure jumps are presented for systems containing N=435136 coarse-grained particles, which correspond to several millions of atoms in a box with linear dimension 447 A . Even for large systems the phase separation can be observed up to the final, macroscopically segregated, equilibrium state. It is shown that in the segregation process the two order parameters of the system (density and concentration) are strongly coupled. The system does not follow the predicted growth law for the characteristic domain size l(t) proportional, variant t in binary fluid mixtures for the range of times accessible in the simulation. Instead, it exhibits a distinctly slower growth, presumably due to the dynamic asymmetry of the constituents.