Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of turbulent flow U. Rasthofer, V. Gravemeier ⇑ Emmy Noether Research Group ‘‘Computational Multiscale Methods for Turbulent Combustion’’, Technische Universität München, Boltzmannstr. 15, 85748 Garching, Germany Institute for Computational Mechanics, Technische Universität München, Boltzmannstr. 15, 85748 Garching, Germany article info Article history: Received 27 January 2012 Received in revised form 13 August 2012 Accepted 11 September 2012 Available online 3 October 2012 Keywords: Large-eddy simulation Multifractal subgrid-scale modeling Variational multiscale method Wall-bounded turbulent flow Turbulent channel flow Backward-facing step Square-section cylinder abstract Multifractal subgrid-scale modeling within a variational multiscale method is proposed for large-eddy simulation of turbulent flow. In the multifractal subgrid-scale modeling approach, the subgrid-scale velocity is evaluated from a multifractal description of the sub- grid-scale vorticity, which is based on the multifractal scale similarity of gradient fields in turbulent flow. The multifractal subgrid-scale modeling approach is integrated into a var- iational multiscale formulation, which constitutes a new application of the variational mul- tiscale concept. A focus of this study is on the application of the multifractal subgrid-scale modeling approach to wall-bounded turbulent flow. Therefore, a near-wall limit of the multifractal subgrid-scale modeling approach is derived in this work. The novel computa- tional approach of multifractal subgrid-scale modeling within a variational multiscale for- mulation is applied to turbulent channel flow at various Reynolds numbers, turbulent flow over a backward-facing step and turbulent flow past a square-section cylinder, which are three of the most important and widely-used benchmark examples for wall-bounded tur- bulent flow. All results presented in this study confirm a very good performance of the pro- posed method. Compared to a dynamic Smagorinsky model and a residual-based variational multiscale method, improved results are obtained. Moreover, it is demonstrated that the subgrid-scale energy transfer incorporated by the proposed method very well approximates the expected energy transfer as obtained from appropriately filtered direct numerical simulation data. The computational cost is notably reduced compared to a dynamic Smagorinsky model and only marginally increased compared to a residual-based variational multiscale method. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Turbulent flow exhibits a complex spatial distribution of eddies, which dictate the evolution of turbulence. An eddy is a structure, for instance, a tube or a sheet, that is formed by the local vorticity and its associated velocity field. The vortices in turbulent flows are then stretched and folded by their self-induced velocity fields as well as the velocity fields induced by all other vortical structures; see, e.g., [1] for elaboration. The repeated stretching and folding of the vorticity field as well as the strain rate represent a multiplicative process within the respective field. As shown in several studies, e.g., [2–4], gradient fields in turbulent flows such as kinetic energy dissipation and enstrophy exhibit multifractal scale similarity, enabling a novel approach to modeling turbulent flow. 0021-9991/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcp.2012.09.013 ⇑ Corresponding author at: Institute for Computational Mechanics, Technische Universität München, Boltzmannstr. 15, 85748 Garching, Germany. Tel.: +49 89 28915245; fax: +49 89 28915301. E-mail addresses: rasthofer@lnm.mw.tum.de (U. Rasthofer), vgravem@lnm.mw.tum.de (V. Gravemeier). Journal of Computational Physics 234 (2013) 79–107 Contents lists available at SciVerse ScienceDirect Journal of Computational Physics journal homepage: www.elsevier.com/locate/jcp