On the Influence of Polynomial De-aliasing on Subgrid Scale Models

Beck, Andrea; Flad, David; Tonhäuser, Claudia; Gassner, Gregor J.; Munz, Claus‐Dieter

doi:10.1007/s10494-016-9704-y

Cited by 34 publications

(33 citation statements)

References 56 publications

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“…We can now apply the elementwise SGWT scale-separation operation to the three-scale VMS-LES approach of Section 2.2. By summing up Equations (20) and (21) and using the all-all approach for the subgrid stress tensor (Table 1), we have…”

Section: Three-scale Wavelet-based Vms-lesmentioning

confidence: 99%

“…This approach was demonstrated by Ramakrishnan and Collis on a turbulent channel flow test case. Modal FEM, in conjunction with three‐scale VMS and the constant‐coefficient Smagorinsky model was tested out for a circular cylinder test case and on the 3D Taylor‐Green vortex (3D‐TGV) . Furthermore, tests using the three‐scale VMS procedure in the framework of mixed finite‐element/finite‐volume methods were carried out, for flows around bluff bodies, in the work of Munts et al and Moussaed et al Finally, we must point out the attempt by Wasberg et al, which utilized a nodal continuous Galerkin (CG) discretization with the Legendre polynomials for the purpose of scale separation for VMS‐LES upon the incompressible channel flow.…”

Section: Introductionmentioning

confidence: 99%

“…Modal FEM, in conjunction with three-scale VMS and the constant-coefficient Smagorinsky model was tested out for a circular cylinder test case 20 and on the 3D Taylor-Green vortex (3D-TGV). 20,21 Furthermore, tests using the three-scale VMS procedure in the framework of mixed finite-element/finite-volume methods were carried out, for flows around bluff bodies, in the work of Munts et al 22 and Moussaed et al 23 Finally, we must point out the attempt by Wasberg et al, 24 which utilized a nodal continuous Galerkin (CG) discretization with the Legendre polynomials for the purpose of scale separation for VMS-LES upon the incompressible channel flow. This approach is very close in philosophy to the approach that we propose in this study; however instead of CG discretization and Legendre polynomials we intend to make use of a DG discretization and second-generation wavelets (SGWs) for the scale separation as will be elaborated in the following.…”

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confidence: 99%

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A wavelet‐based variational multiscale method for the LES of incompressible flows in a high‐order DG‐FEM framework

Pinto

Plata

Lamballais

2019

Numerical Methods in Fluids

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Summary This work focuses upon the development of a wavelet‐based variant of the variational multiscale method (VMS) for accurate and efficient large eddy simulation (LES) called wavelet‐based VMS‐LES (WMS‐LES). This approach has been incorporated within the framework of a high‐order incompressible flow solver based upon the pressure‐stabilized discontinuous Galerkin finite element method (DG‐FEM). The VMS approach is designed to produce an a priori scale separation of the governing equations, in a manner which makes no assumptions on either the boundary conditions or the mesh uniformity. Using second‐generation wavelets (SGWs) elementwise for scale separation ensures, on one hand, the preservation of the computational compactness of the DG‐FEM scheme and, on the other hand, the ability to achieve scale separation in wavenumber space. The optimal space‐frequency localization property of the SGW provides an improvement over the commonly used Legendre polynomials. The suitability of the elementwise SGW scale‐separation operation as a tool for error indication has been demonstrated in an h‐adaptive computation of the reentrant corner test case. Finally, the DG‐FEM solver and the WMS‐LES method have been assessed through simulations upon the three‐dimensional Taylor‐Green vortex test case. Our results indicate that the WMS‐LES approach exhibits a distinct improvement over the monolevel LES approach. This effect is not produced by a change in the magnitude of the subgrid dissipation but rather by the redistribution of the subgrid dissipation in wavenumber space.

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Section: Three-scale Wavelet-based Vms-lesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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A wavelet‐based variational multiscale method for the LES of incompressible flows in a high‐order DG‐FEM framework

Pinto

Plata

Lamballais

2019

Numerical Methods in Fluids

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“…In [34], Chapelier et al have proposed a variational multiscale approach based on a modal DG method and applied it to the Taylor-Green vortex configuration at Re = 3 000. Finally, Beck et al [35] have studied the influence of over-integration on the performance of subgridscale models. The authors demonstrate the benefits of using de-aliasing when a subgrid-scale closure is used at high polynomial degrees.…”

Section: Introductionmentioning

confidence: 99%

On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

2018

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We assess the performance of a high-order discontinuous Galerkin (DG) approach to simulate wall-bounded turbulent flows for a range of Reynolds numbers. First, a plane channel flow configuration with turbulent heat transfer at Re τ = 640 is considered. Second, a detached flow configuration is investigated. This configuration represents the flow over periodically arranged hills. Four bulk Reynolds numbers Re b are considered: 2 800, 10 595, 19 000, and 37 000. For Re b = 2 800 direct numerical simulation (DNS) is used. Large-eddy simulations (LES) based on the WALE subgrid-scale model are carried out for the higher Re b . The simulation results are compared to reference data from CFD and experiment. hp-convergence analyses are performed which demonstrate the superior performance of increasing the polynomial order as compared to refining the mesh. It appears from this work that the use of a subgrid modelling approach together with local hp-adaptation could greatly improve the accuracy of the solution without penalising the computational cost of the simulation.

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“…They thus fundamentally differ from the original VMS idea, that is, the decomposition of the true solution into a discontinuous coarse-scale function space and an accompanying discontinuous fine-scale function space. While several authors have investigated the enhancement of DG methods with fine-scale eddy viscosity or wall models, [25][26][27][28][29][30][31] DG methods based on a residual-based VMS subgrid-scale model are still largely unexplored. To some extent, this may be attributed to the importance of coarse-scale continuity in the derivation of the VMS method.…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin residual‐based variational multiscale method for modeling subgrid‐scale behavior of the viscous Burgers equation

Stoter

Turteltaub

Hulshoff

et al. 2018

Numerical Methods in Fluids

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Summary We initiate the study of the discontinuous Galerkin residual‐based variational multiscale (DG‐RVMS) method for incorporating subgrid‐scale behavior into the finite element solution of hyperbolic problems. We use the one‐dimensional viscous Burgers equation as a model problem, as its energy dissipation mechanism is analogous to that of turbulent flows. We first develop the DG‐RVMS formulation for a general class of nonlinear hyperbolic problems with a diffusion term, based on the decomposition of the true solution into discontinuous coarse‐scale and fine‐scale components. In contrast to existing continuous variational multiscale methods, the DG‐RVMS formulation leads to additional fine‐scale element interface terms. For the Burgers equation, we devise suitable models for all fine‐scale terms that do not use ad hoc devices such as eddy viscosities but instead directly follow from the nature of the fine‐scale solution. In comparison to single‐scale discontinuous Galerkin methods, the resulting DG‐RVMS formulation significantly reduces the energy error of the Burgers solution, demonstrating its ability to incorporate subgrid‐scale behavior in the discrete coarse‐scale system.

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On the Influence of Polynomial De-aliasing on Subgrid Scale Models

Cited by 34 publications

References 56 publications

A wavelet‐based variational multiscale method for the LES of incompressible flows in a high‐order DG‐FEM framework

A wavelet‐based variational multiscale method for the LES of incompressible flows in a high‐order DG‐FEM framework

On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence

A discontinuous Galerkin residual‐based variational multiscale method for modeling subgrid‐scale behavior of the viscous Burgers equation

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