Higher-Order Methods for Compressible Turbulent Flows Using Entropy Variables

Diosady, Laslo T.; Murman, Scott M.

doi:10.2514/6.2015-0294

Cited by 45 publications

(52 citation statements)

References 22 publications

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“…However, the accumulation of energy at the tail of the spectrum is somehow counter intuitive, as we would expect the spectrum to have consistently lower values than in case of the Roe flux. Nevertheless, this result is consistent to what can be observed by Diosady and Murman , where similar behaviour is observed on the Taylor–Green vortex at infinite Reynolds number. Regarding these results, the Lax–Friedrichs flux might be better suited for fully turbulent flows, as it offers a progressive dissipation of the turbulent structures.…”

Section: Assessment On Decaying Homogeneous Isotropic Turbulencesupporting

confidence: 92%

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

Wiart

Hillewaert

Bricteux

et al. 2015

Numerical Methods in Fluids

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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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Section: Assessment On Decaying Homogeneous Isotropic Turbulencesupporting

confidence: 92%

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

Wiart

Hillewaert

Bricteux

et al. 2015

Numerical Methods in Fluids

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“…The nonlinear system for each space-time slab is solved using a preconditioned Jacobian-free approximate Newton-Krylov solver. Further details regarding the space-time DG method can be found in [32][33][34][35]. Note also that no subgrid-scale or wall models are used in the present simulations.…”

Section: Methodsmentioning

confidence: 99%

Scale-Resolving Simulations of Low-Pressure Turbine Cascades With Wall Roughness Using a Spectral-Element Method

Garai

Diosady

Murman

et al. 2018

Volume 2C: Turbomachinery

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The accurate prediction of wall-roughness effects in turbomachinery is becoming critical as turbine designers address airfoil surface quality and degradation concerns arising from the shift to advanced ceramic matrix composite (CMC) or additively-manufactured airfoils operating in higher temperature environments. In this paper, a recently developed computational capability for accurate and efficient scale-resolving simulations of turbomachinery is extended to analyze the boundarylayer separation and transition characteristics in a rough-wall low-pressure turbine (LPT) cascade. The computational capability is based on an entropy-stable discontinuous-Galerkin spectral-element approach that extends to arbitrarily high orders of spatial and temporal accuracy, and is implemented in an efficient manner for a modern high performance computer architecture. Results from the scale-resolving simulations of both smooth and rough airfoil cascades are presented and compared to previous experiments and numerical simulations. The results show that the suction surface boundary layer undergoes laminar separation, transition, and turbulent reattachment for the smooth airfoil cascade, while in the presence of roughness the separation and transition behavior of the suction surface boundary layer is substantially modified. The differences between the smooth and rough airfoil cascades are then highlighted by a detailed analysis of their respective turbulent flow fields.

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“…By applying a test function # with support over an arbitrary space-time volume f2 around a discontinuity A (x, t), we can show that the weak form results in, 4) where J[* is the jump across the discontinuity. Thus the weak form only admits discontinuities subject to the Rankine-Hugoniot condition [20],…”

Section: Weak Solutionsmentioning

confidence: 99%

On the Convergence of Higher-Order Finite Element Methods to Weak Solutions

Couchman

2017

23rd AIAA Computational Fluid Dynamics Conference

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The ability to handle discontinuities appropriately is essential when solving nonlinear hyperbolic partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a discretely conservative scheme. However, discrete conservation is not a strict requirement for convergence to a weak solution. This suggests a hierarchy of discretizations, where discretely conservative schemes are a subset of the larger class of methods that converge to the weak solution. We show here that a range of finite element methods converge to the weak solution without using discrete conservation arguments. The effect of using quadrature rules to approximate integrals is also considered. In addition, we show that solutions using non-conservation working variables also converge to weak solutions. I would also like to thank Professor Spakovszky for letting me TA unified thermodynamics for the last two years. While it was a lot of work, being a TA has been one of the most rewarding parts of my time at MIT so far.

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Higher-Order Methods for Compressible Turbulent Flows Using Entropy Variables

Cited by 45 publications

References 22 publications

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

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

Scale-Resolving Simulations of Low-Pressure Turbine Cascades With Wall Roughness Using a Spectral-Element Method

On the Convergence of Higher-Order Finite Element Methods to Weak Solutions

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