Implicit LES of free and wall‐bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method

Abstract

between the flexibility of industrial finite volume methods (FVMs) and the accuracy of academic solvers, such as high-order finite difference (FDM) or pseudo-spectral (PSM) methods. Because of their computational compacity, most of these methods-in particular, those with discontinuous interpolation-also provide an excellent serial and parallel computational efficiencies. In view of these advantages, it is mainly in the field of scale-resolving simulations of industrial turbulent flows, that is direct numerical simulation (DNS) and large eddy simulation (LES), that these methods offer the best perspectives. Indeed, as DNS and LES require a nearly flawless representation of the (resolved) turbulent scales, current industrial solvers require huge computational resources to provide sufficient accuracy, and hence, up to date, most computations appear to be under-resolved (see Tucker [6,7] for a recent review in turbomachinery).In this paper, we focus on the DGM combined with a symmetric interior penalty (SIP) stabilisation.For the past few years, DGM has been assessed for compressible and incompressible DNS of simple and complex flow configurations [8][9][10]. Those investigations have highlighted the advantages of DGM for these kind of problems. Indeed, the very low dispersion of the method, typical for Galerkin approaches, combined to a dissipation targeted on the smallest scales, offers an accuracy similar to spectral methods (e.g. [11]). These properties also indicate the potential of the method to perform accurate implicit LES (ILES), that is where the dissipation given by the discretisation acts like a subgrid-scale (SGS) model. Several recent publications [12,13], where the method is applied to under-resolved flows, seem to corroborate the accuracy of ILES/DGM. Nevertheless, those studies only validate basic flow statistics (integral values, velocity profiles, etc.) without true reference results and concern transitional rather than fully turbulent conditions. We therefore believe that a validation on more canonical, fully turbulent cases is therefore required to assess whether the ILES/DGM can really compete with state-of-the-art SGS models and academic high-accuracy solvers.This study presents the validation of the compressible version of Argo, the DGM solver developed at Cenaero, for the ILES of equilibrium turbulent flows. The solver has already been intensively assessed for DNS of canonical flows [11] as well as on more industrial cases [14,15], partly during the European FP7 research project IDIHOM. The first sections of the paper describe the numerical method and discuss the ILES strategy. Then, the method is investigated for free turbulent flows on the simulation of homogeneous isotropic turbulence (HIT) at very high Reynolds number. Very few studies on HIT using unstructured high-order methods can be found in literature and the conclusions are not directly applicable to the discretisation and LES approach under study here. To our knowledge, only one publication is dedicated to the assessment of LES of ...

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