Comparison of stabilization strategies applied to scale-resolved simulations using the discontinuous Galerkin Method

Discontinuous Galerkin; Discontinuous Galerkin Spectral Element Method; Entropy stability; Budget Kinetic Energy; Turbulence; Transonic flows; Artificial Viscosity

Abstract :

[en] This study evaluates several stabilization strategies for the discontinuous Galerkin Spec- tral Element Method in scale-resolved simulations of compressible turbulence, with em- phasis on accuracy, robustness, and computational efficiency. A novel selective entropy- stable approach (DG-ES) is introduced, which activates entropy stabilization only in localized regions to enhance robustness while minimizing dissipation. The performance of DG-ES is benchmarked against artificial viscosity (DG-AV), as well as fully entropy- stable methods based on Gauss–Legendre (ESDG-GL) and Gauss–Lobatto (ESDG-GLL) quadratures, across a range of canonical shock–turbulence interaction test cases. Results show that DG-AV performs well in scenarios involving highly mobile shocks, effectively resolving both shocks and small-scale turbulence, but its accuracy deteriorates in sta- tionary shock configurations. Additionally, DG-AV is highly sensitive to the choice and calibration of its detector. In contrast, entropy-stable methods improve post-shock turbu- lence accuracy but tend to introduce spurious oscillations near shocks and incur greater computational cost. The ESDG-GL method suffers from entropy projection errors in shocklet-dominated regions, while ESDG-GLL is affected by excess dissipation due to under-integration. DG-ES achieves a favorable balance, accurately capturing turbulence with reduced sensitivity to detector calibration and maintaining competitive efficiency. However, like the ESDG-GL, it requires smaller time steps to ensure stability in the presence of strong shocks, due to the stiffness introduced by the entropy projection.

Research Center/Unit :

A&M - Aérospatiale et Mécanique - ULiège

Disciplines :

Aerospace & aeronautics engineering

Author, co-author :

Bilocq, Amaury ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Borbouse, Maxime ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Levaux, Nayan ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Terrapon, Vincent ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Modélisation et contrôle des écoulements turbulents

Hillewaert, Koen ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)

Language :

English

Title :

Comparison of stabilization strategies applied to scale-resolved simulations using the discontinuous Galerkin Method

Publication date :

17 July 2025

Journal title :

Journal of Computational Physics

ISSN :

0021-9991

eISSN :

1090-2716

Publisher :

Elsevier, Atlanta, Georgia

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique

Available on ORBi :

since 17 July 2025

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