Effects of Upwinding in Large Eddy Simulation of Turbulent Flows

Abstract

In this paper a new adaptive upwinding method, compatible with the available numerical scheme, is developed and implemented. This method improves the results of large eddy simulation (LES) by adjusting the contribution of upwinding term to the convective flux. This adjustment is essentially controlled by the intensity of the local wiggle. This work is an attempt to study and evaluate the numerical dissipation of the available low order numerical tool and to prepare and improve this tool for the purpose of LES. At first, the available finite element/volume numerical code, previously used for the Reynolds-averaged Navier–Stokes (RANS) simulations of compressible flows, is extensively studied, using channel flow stability test and decaying isotropic turbulence. The goal is to use these numerical tests in order to investigate the ability of the numerical tool in order to emulate necessary turbulent characteristic. The new adaptive upwinding method is then introduced in order to improve the results. In addition, a review of the main aspects of LES of turbulent flows such as cascade of energy from high to low scale eddies, effects of subgrid modeling, numerical dissipation, accuracy and stability, is also presented. It has been a main concern in our work to choose those numerical tests which are relatively simple and don’t require very high computational efforts, but are also viable enough to show main features necessary to assess the performance of the numerical scheme. I. Introduction The Navier–Stokes equations (NSE), supplemented by empirical laws for the dependence of viscosity and thermal conductivity to other flow variables and by a constitutive law defining how the pressure depends on the other flow variables, can be used to describe all flow phenomena in a linear viscous fluid. In addition, appropriate initial and boundary conditions must be supplied to ensure the well-posedness of the NSE and to select the specific physical flow realization which is going to be emulated. From a computational point of view, the NSE can be solved directly (without any need for filtration or averaging) for laminar flows, while for turbulent flows the wide range of eddy scales, required to be captured, prohibits direct numerical simulation (DNS). That’s specially the case for high Reynolds numbers. 18 , 17 Therefore direct numerical simulation of turbulent flows is still far out of range for flows of practical industrial interest and most of the DNS simulations reported in the literature are limited to simple geometries and moderate Reynolds numbers. Moreover, some of the recommendations given in the literature calling for required highly resolved grids and high-order numerical schemes are clearly difficult to respect in an industrial context. 12