Numerical analysis of homogeneous and isotropic turbulence by using the third order upwind finite-difference method. Study in wave number space.

概要

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By using the third order upwind finite-difference method for the convective term in a Navier-Stokes equation, numerical stability can be improved because of the numerical viscosity which is proportional to the fourth derivative of velocity. So high Reynolds number turbulent flow can be simulated directly without any explicit turbulent models. In this study, homogeneous and isotropic turbulent flow is simulated by this method, and the calculated results are compared with experimental data. As a result, it is shown that this method is equivalent to the method in which basic equations are spatially averaged by a filtering operation, and this equivalent filter width is a function of the mesh size and the coefficient of the numerical viscosity term. Energy spectra and turbulent kinetic energy of the calculated results are in good agreement with the experimental data when filtering operation is taken into account.
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