On implicit turbulence modeling for LES of compressible flows

Abstract

The subgrid-scale (SGS) model in a large-eddy simulation (LES) generally operates on a range of scales that is marginally resolved by discretization schemes. Consequently, the discretization scheme’s truncation error and the subgrid-scale model are linked, which raises the question of how accurate the computational results are. On the other hand, the link between the SGS model and truncation error can be beneficially exploited by developing discretization methods for subgrid-scale modeling, or vice versa. Approaches where the SGS model and the numerical discretization scheme are fully merged are called implicit LES (ILES) methods. Implicit SGS modeling requires procedures for design, analysis, and optimizationof nonlinear discretization schemes. In order to improve on the aforementioned modeling uncertainties, we have proposed a systematic framework for implicit LES. The resulting adaptive local deconvolution method (ALDM) for implicit LES is based on a nonlinear deconvolution operator and a numerical flux function [1, 4]. Free parameters inherent to the discretization allow to control the truncation error. They are calibrated in such a way that the truncation error acts as a physically motivated SGS model. ALDM has shown the potential for providing a reliable, accurate, and efficient method for LES. Various applications, such as three-dimensional homogeneous isotropic turbulence, transitional and turbulent plane channel flow, and turbulent boundarylayer separation, demonstrate the good performance of the implicit model. Computational results show that a carefully designed implicit SGS model can perform at least as well as established explicit models, for most considered applications the performance is actually even better. This is possible because physical reasoning is incorporated into the design of the discretization scheme and discretization effects are fully taken into account within the SGS model formulation. The method is established for LES of turbulent flows governed by the incompressible Navier-Stokes equations and for passive-scalar mixing [3, 5]. The subject of this paper is the extension of the methodology to ILES of compressible turbulence.KeywordsTruncation ErrorDiscretization SchemeCompressible TurbulenceTurbulent Mach NumberPlane Channel FlowThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.