Turbulent diffusion of temperature in the homogeneous and isotropic turbulence. Numerical analysis by using a third order upwind scheme.

Abstract

By using the third order upwind finite-difference scheme for the convective term in the Navier-Stokes equation, numerical stability can be improved, because of the numerical viscosity, which is proportional to the fourth derivative of the velocity. In this study, this method is applied to the simulation of homogeneous and isotropic turbulent flow with a passive scalar mixing. The calculated results are compared with the filtered experimental results. As for the velocity, it is shown that the energy spectrum of the calculated results are in good agreement with the filtered experimental ones. But this scheme predicts a too small decay of the temperature fluctuation in the low wave number region compared with the filtered experimental results. This problem is solved by using the sub grid scale model as the numerical diffusion term. The temperature fluctuation spectrum and the temperature fluctuation energy of the calculated results are in good agreement with those of the filtered experimental ones.