Computational Fluid Dynamics simulations of the thermodiffusion in high pressure ternary hydrocarbon mixtures of methane, n-butane and n-dodecane subject to micro-vibrations at reduced gravity are presented. Micro-gravity investigations of mixtures at such high pressures are unprecedented. The simulations indicate a formation of a single convective cell in all the mixtures due to a steady static micro-gravity in the x and y directions, and a stronger velocity component orthogonal to the direction of the temperature gradient. The consequent separation behavior of methane and n-dodecane in terms of the concentration profiles as well as the thermodiffusion coefficients was in agreement with the experimental trends. Also, as in the experiments, the change in the sign of the thermodiffusion coefficient of n-butane was correctly predicted. Small discrepancy was observed in the concentration profile of n-butane and is due to the under prediction of the thermodiffusion coefficients by the current thermodiffusion model as well as the displacement of small traces of n-butane via the bulk flow of n-dodecane.