ESTIMATION OF CONVECTION ERRORS OF FINITE DIFFERENCE METHODS FOR COMPRESSIBLE TURBULENCE SIMULATIONS

摘要

The performance of several different numerical methods previously used or employed for large-eddy or direct simulations of compressible flows is analytically considered. The approach uses the von Neumann method to obtain the spectral amplification factor for each scheme for the linearized Euler equations. This estimate of the convection error per time step is then integrated over one eddy time scale for the conditions of a transonic, high Reynolds number problem. The results are used to analytically estimate the error from the numerical schemes by reference to an approximate spectrum of the turbulence obtained from isotropic homogeneous turbulence theory. The numerical methods considered include the McCormack scheme (second and fourth order), a second-order flux-corrected-transport scheme, a fourth-order Runge-Kutta, centered-space scheme, a high order implicit upwind method and a sixth-order Pade method. The results show significant differences in the stability and resolution characteristics of the various methods. In conjunction with conventional tests for compressible flow methods, the present approach may provide improved a priori evaluation of proposed methods for large-eddy and direct numerical simulations of turbulence in compressible flows.