Effects of the Order of Accuracy of Finite-Difference Method and Grid Resolution on LFS of Wall Turbulence.

Abstract

In the large eddy simulation (LES) of turbulent flow, grid scale (GS) flow field is described by solving discretized governing equations of flow motion with a subgrid scale (SGS) model. Hence, the reliability of the LES data depends strongly not only on the reliability of the SGS model but also on the accuracy of the numerical method. In the LES a finite difference method (FDM) is widely used for practical problems. However, the truncation error of FDM is usually not so small compared with the SGS stress. The problem can be removed by increasing grid resolution, but it is still difficult to keep enough grid resolution in the LES of high Reynolds number flows. In this study, the effects of the order of accuracy of FDM and grid resolution on the LES of plane channel turbulent flow are estimated by the fully conservative higher order staggered FDM scheme proposed recently. The simulations of the flow at Rer=100 are submitted without SGS model with various grid resolution and several order of FDM up to 12th-order accuracy, and the fact that the FDM discretization has the effects of both truncation error and sharp cutoff is revealed. The effect of truncation error decreases the wall friction loss, while the effect of sharp cutoff increases it. Then, the flow at Rer=180 is simulated with the dynamic SGS model, and it is pointed out that we have to take the numerical error into consideration in constructing the SGS model for LES of practical problems.