Discontinuous Galerkin Methods for Compressible DNS

Collis, S. Scott; Ghayour, Kaveh

doi:10.1115/fedsm2003-45632

Cited by 18 publications

(18 citation statements)

References 17 publications

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“…For the forcing term, Galerkin projections of the Fourier components were carried analytically through the relations given in Eqs. (15)(16)(17). These projections were however numerically stripped from the secondary modes originating from each single Fourier component by means of a 'filtering' procedure based on the system of eigenmodes discussed in Sec.…”

Section: Experiments In Burgers Turbulencementioning

confidence: 99%

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

Moura

Sherwin

Peiró

2015

Journal of Computational Physics

145

109

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Please cite this article in press as: R.C. Moura et al., Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods, J. Comput. Phys. (2015), http://dx.doi. org/10.1016/j.jcp.2015.06.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Linear dispersion-diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods R.C. Moura, S.J. Sherwin 1 , J. PeiróWe investigate the potential of linear dispersion-diffusion analysis in providing direct guidelines for turbulence simulations through the under-resolved DNS (sometimes called implicit LES) approach via spectral/hp methods. The discontinuous Galerkin (DG) formulation is assessed in particular as a representative of these methods. We revisit the eigensolutions technique as applied to linear advection and suggest a new perspective on the role of multiple numerical modes, peculiar to spectral/hp methods. From this new perspective, "secondary" eigenmodes are seen to replicate the propagation behaviour of a "primary" mode, so that DG's propagation characteristics can be obtained directly from the dispersion-diffusion curves of the primary mode. Numerical dissipation is then appraised from these primary eigencurves and its effect over poorly-resolved scales is quantified. Within this scenario, a simple criterion is proposed to estimate DG's effective resolution in terms of the largest wavenumber it can accurately resolve in a given hp approximation space, also allowing us to present points per wavelength estimates typically used in spectral and finite difference methods. Although strictly valid for linear advection, the devised criterion is tested against (1D) Burgers turbulence and found to predict with good accuracy the beginning of the dissipation range on the energy spectra of under-resolved simulations. The analysis of these test cases through the proposed methodology clarifies why and how the DG formulation can be used for under-resolved turbulence simulations without explicit subgrid-scale modelling.In particular, when dealing with communication limited hardware which forces one to consider the performance for a fixed number of degrees of freedom, the use of higher polynomial orders along with moderately coarser meshes is shown to be the best way to translate available degrees of freedom into resolution power.

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Section: Experiments In Burgers Turbulencementioning

confidence: 99%

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

Moura

Sherwin

Peiró

2015

Journal of Computational Physics

145

109

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“…), the number of reported successful DG simulations for both incompressible and compressible cases is small. Collis in 2002 was among the first to use high‐order DG methods for the DNS of compressible flows, and he applied a Smagorinsky eddy viscosity model to the small scales via the variational multiscale method in a LES . More recently, Uranga et al , used an N = 3 DG formulation for the simulation of a transitional flow over an airfoil, taking advantage of the numerical dissipation to account for the damping action of the unresolved scales in an implicit LES approach.…”

Section: Introductionmentioning

confidence: 99%

High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

Beck

Bolemann

Flad

et al. 2014

Numerical Methods in Fluids

211

142

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SUMMARYIn this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under‐resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high‐order spectral methods by using high‐order ansatz functions up to 12th order. We employ polynomial de‐aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high‐order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at ReD=3900, a confined periodic hill flow at Reh=2800 and the transitional flow over a SD7003 airfoil at Rec=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright © 2014 John Wiley & Sons, Ltd.

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“…Volker et al [3]. Interestingly, Collis [4] has shown experiments where weak boundary conditions give smaller errors than strong boundary conditions.…”

Section: Introductionmentioning

confidence: 97%

Weak imposition of boundary conditions for the Navier–Stokes equations by a penalty method

Çağlar¹,

Liakos²

2008

Numerical Methods in Fluids

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SUMMARYWe prove convergence of the finite element method for the Navier-Stokes equations in which the no-slip condition and no-penetration condition on the flow boundary are imposed via a penalty method. This approach has been previously studied for the Stokes problem by Liakos (Weak imposition of boundary conditions in the Stokes problem. Ph.D. Thesis, University of Pittsburgh, 1999). Since, in most realistic applications, inertial effects dominate, it is crucial to extend the validity of the method to the nonlinear Navier-Stokes case. This report includes the analysis of this extension, as well as numerical results validating their analytical counterparts. Specifically, we show that optimal order of convergence can be achieved if the computational boundary follows the real flow boundary exactly.

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Discontinuous Galerkin Methods for Compressible DNS

Cited by 18 publications

References 17 publications

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

Linear dispersion–diffusion analysis and its application to under-resolved turbulence simulations using discontinuous Galerkin spectral/hp methods

High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations

Weak imposition of boundary conditions for the Navier–Stokes equations by a penalty method

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