Spectral compact difference hybrid computation of passive scalar in isotropic turbulence

An accurate and efficient hybrid numerical method is developed for direct numerical simulation of passive scalar in homogeneous turbulence for the Schmidt number 1 and 50. The hybrid method uses the standard Fourier spectral method for the incompressible Navier–Stokes equation and the combined compact difference scheme for the passive scalar transport equation. Accuracy of the method is carefully examined by comparing with the full spectral method regarding the spectra, probability density function, field structure of the passive scalar, and is found to be very satisfactory. The computational time for the hybrid method is decreased by 26% for the Schmidt number 1 when compared to the full spectral method, and by 77% for the Schmidt number 50 when the number of grid points for the velocity field is reduced under the scale separation.