An Adaptive Variational Multiscale Discontinuous Galerkin Method For Large Eddy Simulation

Kuru, G.; Plata, Marta de la Llave; Couaillier, Vincent; Abgrall, Rémi; Coquel, Fré́dé́ric

doi:10.2514/6.2016-0584

Cited by 17 publications

(17 citation statements)

References 15 publications

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“…The first refinement indicator that we consider in this work was developed by Kuru et al 2 in the context of the variational multiscale simulation (VMS) approach. 36 In the VMS framework the numerical solution vector u h is expressed as:…”

Section: Iiia1 the Vms Indicatormentioning

confidence: 99%

A comparison of refinement indicators for p-adaptive discontinuous Galerkin methods for the Euler and Navier-Stokes equations

Naddei¹,

Plata²,

Couaillier³

2018

2018 AIAA Aerospace Sciences Meeting

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This paper presents an analysis of refinement indicators for the numerical solution of the Euler and the Navier-Stokes equations using a p-adaptive discontinuous Galerkin (DG) method. Residual error, discretization error and feature-based indicators are studied in the context of p-adaptive DG simulations of two inviscid flow configurations, namely, the flow over a Gaussian bump and the flow past a circular cylinder. As expected, the superiority of local p-refinement as compared to uniform p-refinement is clearly observed. The results obtained highlight the efficiency of the considered refinement indicators with respect to an indicator based on the local entropy error. In particular, they identify regions where numerical errors are being produced and not those where errors are being convected. Finally the p-adaptive algorithm is applied to the simulation of the laminar flow past a circular cylinder at Re = 40. The great potential of the spectral decay 1 and VMS 2 indicators, which combine accuracy and computational efficiency, is also demonstrated.

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Section: Iiia1 the Vms Indicatormentioning

confidence: 99%

A comparison of refinement indicators for p-adaptive discontinuous Galerkin methods for the Euler and Navier-Stokes equations

Naddei¹,

Plata²,

Couaillier³

2018

2018 AIAA Aerospace Sciences Meeting

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“…The remaining lower-level scaling function and multiwavelet coefficients can be obtained by successively applying the quadrature mirror filter coefficients [26] developed in Eq. (29), which in the particular case of two levels results 0…”

Section: B Building Local Hierarchy Via Mwsmentioning

confidence: 97%

Local Multiwavelet-Based Adaptation within a Discontinuous Galerkin Framework

Bautista¹,

Plata²,

Couaillier³

et al. 2021

AIAA Scitech 2021 Forum

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The main goal of the proposed research is to investigate and develop error estimators and mesh adaptation strategies within a discontinuous Galerkin (DG) formulation in order to reduce the computational cost, for a prescribed level of accuracy. We are interested in how multiwavelets (MWs) and their properties may shed new light on the adaptation process. This is motivated by the fact that MWs break any input apart into a hierarchy of low resolution data and subsequently finer details. Our error estimator makes use of MWs' properties while being local to the element, maintaining the parallel efficiency of the solver. Early tests on the one-dimensional viscous Burgers' equation show promising results. This work will be focused on a backward-facing step configuration to assess the performance of the method in higher dimensions.

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“…We choose the Green's function defined in (28) as the test function w ′ . Substituting G(x, y) in place of w ′ in (27), we obtain…”

Section: General Form Of the Fine-scale Volumetric Modelmentioning

confidence: 99%

“…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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An Adaptive Variational Multiscale Discontinuous Galerkin Method For Large Eddy Simulation

Cited by 17 publications

References 15 publications

A comparison of refinement indicators for p-adaptive discontinuous Galerkin methods for the Euler and Navier-Stokes equations

A comparison of refinement indicators for p-adaptive discontinuous Galerkin methods for the Euler and Navier-Stokes equations

Local Multiwavelet-Based Adaptation within a Discontinuous Galerkin Framework

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

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