In this paper, the spectrum of high Schmidt number passive scalar in forced homogeneous isotropic turbulence is studied through direct numerical simulations. An hybrid spectral-particle method is used with a finer resolution of the scalar than of the momentum and large time-steps. This approach enables to perform a systematic analysis over a wide range of Schmidt numbers. Our results recover the theoretical scaling for the variance scalar spectrum, and its relationship with the value of the Schmidt number, for large, intermediate and small scales. The influence of the form of the scalar forcing is also discussed.
