A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation

arXiv:0709.0372v1 [physics.flu-dyn] 4 Sep 2007 A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation Marc A. Habisreutinger a, Roland Bouffanais a,∗,1, Emmanuel Leriche a, Michel O. Deville a aLaboratory of Computational Engineering, ´Ecole Polytechnique F´ed´erale de Lausanne, STI – ISE – LIN, Station 9, CH–1015 Lausanne, Switzerland Abstract Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legen- dre spectral element method is used for the spatial discretization to solve the fil- tered Navier–Stokes equations. A novel variant of approximate deconvolution mod- els blended with a mixed scale model using a dynamic evaluation of the subgrid- viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12’000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid- driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dis- persion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability. Key words: Large-eddy simulation, approximate deconvolution models, dynamic mixed scales model, lid-driven cavity, spectral element methods. Article published in J. Comput. Phys. 224 (2007) 241–276 1 Introduction Large-eddy simulation (LES) represents a way of reducing the number of de- grees of freedom of the simulation with respect to the requirements of the direct numerical simulation (DNS). This is done by calculating only low-frequency modes in space and modeling high-frequency ones, the scale separation be- ing performed by filtering in space the Navier–Stokes equations. Large-scale structures are obtained by the computed flow dynamics while the behavior of subgrid scales and their interaction with large eddies are modeled by the additional term in the LES governing equations resulting from filtering the Navier–Stokes equations. The expression of the additional term as a function of the resolved field is referred to as subgrid modeling. Approximate deconvolution models (ADM) constitute a particular family of subgrid models. They rely on the attempt to recover, at least partially, the original unfiltered fields, up to the grid level, by inverting the filtering operator applied to the Navier–Stokes equations. The focus here is on the approximate iterative method introduced by Stolz and Adams [1] which is based on the van Cittert procedure. This method was subsequently applied to incompress- ible wall-bounded flows [2], to compressible flows and to shock-boundary layer interaction [3] using a new variant ADM-RT, blending ADM with a relax- ation term (RT) increasing the dissipative character of the model. Transitional flows were also investigated by Schlatter et al. [4]. Over the past five years, ADM spread over various fields of application. Gullbrand and Chow studied the effect of explicit filtering in the case of channel flow [5]. ADM were also more recently applied to the LES of a rectangular jet and to computational aero-acoustics by Rembold and Kleiser [6]. Particle-laden turbulent flows were investigated in the ADM framework by Shotorban and Mashayek [7]. From the numerical viewpoint, Schlatter et al. [4] used a parallel implementation of a mixed Fourier-Chebyshev spectral method. These models were also im- plemented in a finite volume framework in the semi-industrial code NSMB, Navier–Stokes Multi–Block, by von Kaenel et al. who applied it to shock- boundary layer interaction and channel flow in [8, 9]. To our knowledge, the only implementation based on the spectral element method (SEM) is due to Iliescu and Fischer [10] who used ADM based on the rational LES model (RLES) instead of the van Cittert one. More recently, Pruett et al. proposed a temporal ADM for LES [11] and a stability analysis of the LES-ADM equa- tions was performed by Dunca and Epshteyn [12]. ∗Corresponding author. Email addresses: marc-antoine.habisreutinger@epfl.ch (Marc A. Habisreutinger), roland.bouffanais@epfl.ch (Roland Bouffanais), emmanuel.leriche@epfl.ch (Emmanuel Leriche), michel.deville@epfl.ch (Michel O. Deville). 1 Supported by a Swiss National Science Foundation Grant No. 200020–101707 242 LES of Newtonian incompressible fluid flows with ADM based on the van Cit- tert method using Legendre-SEM as spatial discretization to solve the filtered Navier–Stokes equations are env

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