Turbulence simulations with an improved interior penalty discontinuous Galerkin method and SST k-ω model

• Published in: Computers & fluids 2023-09, Vol.263, p.105967, Article 105967
• Main Authors: Zhao, Ming, Wei, Tong, Hao, Shixi, Ding, Qiushi, Liu, Wei, Li, Xiaojian, Liu, Zhengxian
• Format: Article
• Language: English
• Subjects: Computational Fluid Dynamics; Discontinuous Galerkin method; interior penalty method; RANS simulation
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2023.105967

•Turbulence simulations have been conducted in the present study with an improved IPDG method and SST k-ω model.•The improved IPDG method was introduced here to eliminate the fourth-order homogeneity tensor connecting the viscous terms and the variable gradients.•The effectiveness and applicability of our improved IPDG method with SST k-ω turbulence model have been comprehensively validated under subsonic, transonic and supersonic conditions. The feasibility of high-precision interior penalty discontinuous Galerkin (IPDG) method is still questionable when SST k-ω model and its compressibility correction are adopted. To this end, turbulence simulations with an improved IPDG method and SST k-ω model have been conducted in the present study. In detail, the improved IPDG method was first introduced to eliminate the fourth-order homogeneity tensor connecting the viscous terms and variable gradients. The numerical accuracy has been systematically validated with several canonical cases. To overcome the numerical instability problem coming along with turbulence model simulation, a hybrid approach was implemented. Actually, finite volume method was utilized here for SST k-ω model. Then, the accuracy and reliability of the improved IPDG method have been analyzed in accompany with SST k-ω model and its compressibility correction. Actually, simulations of subsonic, transonic and supersonic cases have been conducted, including plate/airfoil boundary layers and shear layers. The accuracy has been comprehensively validated through quantitative comparison with experimental data, while the superiority of the compressibility correction could be observed at high Mach number.