| Citation: | ZHAO Ming, XIAO Jiabing, DING Qiushi, et al. Large eddy simulation of channel flows based on IPDG method and subgrid model estimation[J]. Journal of Aerospace Power, 2025, 40（5）：20230693 doi: 10.13224/j.cnki.jasp.20230693
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Based on the method framework of the high-accuracy interior penalty discontinuous Galerkin (IPDG) finite element, combined with large eddy simulation (LES), a numerical simulation study was conducted on channel flows. Four different subgrid scale models (Smagorinsky model, Smagorinsky model with Van Driest damping function, wall-adapting local eddy-viscosity (WALE) model, and dynamic model) were employed, and the simulated Mach numbers were 0.2 and 0.7, corresponding to incompressible flow and weak compressible flow, respectively. The results indicated that, within the improved IPDG-LES framework, the Smagorinsky model exhibited lower accuracy due to its excessive dissipation characteristics within the boundary layer. The Smagorinsky model with a dumping function can improve the accuracy but still exhibited excessive viscosity near the wall. The results of WALE model and dynamic models generally outperformed the aforementioned Smagorinsky models and were closer to the reference data, with the dynamic model performing the best overall. Additionally, different models led to similar performances at Mach numbers of 0.2 and 0.7, indicating good adaptability of current IPDG-LES method to weak compressible flows.
| [1] |
KIM J,MOIN P,MOSER R. Turbulence statistics in fully developed channel flow at low Reynolds number[J]. Journal of Fluid Mechanics,1987,177: 133-166. doi: 10.1017/S0022112087000892
|
| [2] |
MOSER R D,KIM J,MANSOUR N N. Direct numerical simulation of turbulent channel flow up to Reτ=590[J]. Physics of Fluids,1999,11(4): 943-945. doi: 10.1063/1.869966
|
| [3] |
COLEMAN G N,KIM J,MOSER R D. A numerical study of turbulent supersonic isothermal-wall channel flow[J]. Journal of Fluid Mechanics,1995,305: 159-183. doi: 10.1017/S0022112095004587
|
| [4] |
WEI L,POLLARD A. Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method[J]. Computers & Fluids,2011,47(1): 85-100.
|
| [5] |
YANG X Q,CHENG J,WANG C,et al. A fast,implicit discontinuous Galerkin method based on analytical Jacobians for the compressible Navier-Stokes equations[R]. AIAA-2016-1326,2016.
|
| [6] |
贺立新,张来平,张涵信. 任意单元间断Galerkin有限元计算方法研究[J]. 空气动力学学报,2007,25(2): 157-162. HE Lixin,ZHANG Laiping,ZHANG Hanxin. Discontinuous Galerkin finite element method on 3D arbitrary elements[J]. Acta Aerodynamica Sinica,2007,25(2): 157-162. (in Chinese
HE Lixin, ZHANG Laiping, ZHANG Hanxin. Discontinuous Galerkin finite element method on 3D arbitrary elements[J]. Acta Aerodynamica Sinica, 2007, 25(2): 157-162. (in Chinese)
|
| [7] |
JIANG Z H,YAN C,YU J. High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations[J]. Applied Mathematics and Mechanics,2014,35(7): 799-812. doi: 10.1007/s10483-014-1834-9
|
| [8] |
吕宏强,张涛,孙强,等. 间断伽辽金方法在可压缩流数值模拟中的应用研究综述[J]. 空气动力学学报,2017,35(4): 455-471. LYU Hongqiang,ZHANG Tao,SUN Qiang,et al. Applications of discontinuous Galerkin method in numerical simulations of compressible flows: a review[J]. Acta Aerodynamica Sinica,2017,35(4): 455-471. (in Chinese
LYU Hongqiang, ZHANG Tao, SUN Qiang, et al. Applications of discontinuous Galerkin method in numerical simulations of compressible flows: a review[J]. Acta Aerodynamica Sinica, 2017, 35(4): 455-471. (in Chinese)
|
| [9] |
秦望龙,吕宏强,陈正武. 基于间断galerkin有限元方法的高精度流场数值模拟研究[C]//2016年度全国气动声学学术会议论文摘要集. 北京:中国航空学会航空声学分会,2016: 212-218. QIN Wanglong,LYU Hongqiang,CHEN Zhengwu. Research on high-precision numerical simulation of flow field based on discontinuous galerkin finite element method [C]//2016 National Conference on AeroAcoustics Abstracts,Beijing:Acoustics Technical Committee,Chinese Society of Aeronautics and Astronautics,2016: 212-218. (in Chinese
QIN Wanglong, LYU Hongqiang, CHEN Zhengwu. Research on high-precision numerical simulation of flow field based on discontinuous galerkin finite element method [C]//2016 National Conference on AeroAcoustics Abstracts, Beijing: Acoustics Technical Committee, Chinese Society of Aeronautics and Astronautics, 2016: 212-218. (in Chinese)
|
| [10] |
BASSI F,REBAY S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible navier-stokes equations[J]. Journal of Computational Physics,1997,131(2): 267-279. doi: 10.1006/jcph.1996.5572
|
| [11] |
BASSI F,REBAY S,MARIOTTI G,et al. A high-order accurate discontinuous finite element method for inviscid and viscous turbomachinery flows[C]//2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics. Antwerpen,Belgium: Technologisch Instituut,1997: 99-108.
|
| [12] |
COCKBURN B,SHU C W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems[J]. SIAM Journal on Numerical Analysis,1998,35(6): 2440-2463. doi: 10.1137/S0036142997316712
|
| [13] |
HARTMANN R,HOUSTON P. Symmetric interior penalty DG methods for the compressible Navier-stokes equations I: method formulation method formulation[J]. International Journal of Numerical Analysis & Modeling,2006,3(1): 1-20.
|
| [14] |
HARTMANN R,HOUSTON P. Symmetric interior penalty DG methods for the compressible Navier-Stokes equations Ⅱ: goal-oriented a posteriori error estimation [J]. International Journal of Numerical Analysis & Modeling,2006,3(2): 141-162.
|
| [15] |
赵博,赵明,刘伟,等. 基于IPDG方法的嵌套网格技术[J]. 航空动力学报,2022,37(6): 1206-1216. ZHAO Bo,ZHAO Ming,LIU Wei,et al. Chimera grid technology with IPDG method[J]. Journal of Aerospace Power,2022,37(6): 1206-1216. (in Chinese
ZHAO Bo, ZHAO Ming, LIU Wei, et al. Chimera grid technology with IPDG method[J]. Journal of Aerospace Power, 2022, 37(6): 1206-1216. (in Chinese)
|
| [16] |
王贤,刘伟,赵明,等. 基于IPDG方法的超声速混合层流动数值模拟[J]. 航空动力学报,2021,36(2): 275-283. WANG Xian,LIU Wei,ZHAO Ming,et al. Numerical simulations of supersonic mixing layers with IPDG method[J]. Journal of Aerospace Power,2021,36(2): 275-283. (in Chinese
WANG Xian, LIU Wei, ZHAO Ming, et al. Numerical simulations of supersonic mixing layers with IPDG method[J]. Journal of Aerospace Power, 2021, 36(2): 275-283. (in Chinese)
|
| [17] |
PLATA M D L L,COUAILLIER V,LE PAPE M C. On the use of a high-order discontinuous Galerkin method for DNS and LES of wall-bounded turbulence[J]. Computers & Fluids,2018,176: 320-337.
|
| [18] |
DE WIART C C,HILLEWAERT K,BRICTEUX L,et al. Implicit LES of free and wall-bounded turbulent flows based on the discontinuous Galerkin/symmetric interior penalty method[J]. International Journal for Numerical Methods in Fluids,2015,78(6): 335-354.
|
| [19] |
LENORMAND E,SAGAUT P,PHUOC L T,et al. Subgrid-scale models for large-eddy simulations of compressible wall bounded flows[J]. AIAA Journal,2000,38(8): 1340-1350. doi: 10.2514/2.1133
|
| [20] |
BECK A D,FLAD D G,TONHÄUSER C,et al. On the influence of polynomial de-aliasing on subgrid scale models[J]. Flow,Turbulence and Combustion,2016,97(2): 475-511. doi: 10.1007/s10494-016-9704-y
|
| [21] |
ABBÀ A,BONAVENTURA L,NINI M,et al. Dynamic models for Large Eddy Simulation of compressible flows with a high order DG method[J]. Computers & Fluids,2015,122: 209-222.
|
| [22] |
DEARDORFF J W. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers[J]. Journal of Fluid Mechanics,1970,41: 453-480. doi: 10.1017/S0022112070000691
|
| [23] |
MOIN P,SQUIRES K,CABOT W,et al. A dynamic subgrid-scale model for compressible turbulence and scalar transport[J]. Physics of Fluids A,1991,3(11): 2746-2757. doi: 10.1063/1.858164
|
| [24] |
PIOMELLI U,ZANG T A,SPEZIALE C G,et al. On the large-eddy simulation of transitional wall-bounded flows[J]. Physics of Fluids A: Fluid Dynamics,1990,2(2): 257-265. doi: 10.1063/1.857774
|
| [25] |
NICOUD F,DUCROS F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor[J]. Flow,Turbulence and Combustion,1999,62(3): 183-200. doi: 10.1023/A:1009995426001
|
| [26] |
GERMANO M,PIOMELLI U,MOIN P,et al. A dynamic subgrid-scale eddy viscosity model[J]. Physics of Fluids A: Fluid Dynamics,1991,3(7): 1760-1765. doi: 10.1063/1.857955
|
| [27] |
ZHAO Ming,WEI Tong,HAO Shixi,et al. Turbulence simulations with an improved interior penalty discontinuous Galerkin method and SST k-ω model[J]. Computers & Fluids,2023,263: 105967.
|
| [28] |
PIOMELLI U,CHASNOV J R. Large-eddy simulations: theory and applications[M]//HALLBÄCK M,HENNINGSON D S,JOHANSSON A V,et al. Turbulence and Transition Modelling. Dordrecht: Springer,1996: 269-336.
|
| [29] |
LENORMAND E,SAGAUT P,PHUOC L. Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number[J]. International Journal for Numerical Methods in Fluids,2000,32(4): 369-406. doi: 10.1002/(SICI)1097-0363(20000229)32:4<369::AID-FLD943>3.0.CO;2-6
|
| [30] |
DUPUY D,TOUTANT A,BATAILLE F. A posteriori tests of subgrid-scale models in an isothermal turbulent channel flow[J]. Physics of Fluids,2019,31(4): 1-26.
|
| [31] |
GU Z,JIAO J,ZHANG Y,et al. Large eddy simulation using a dynamic mixing length subgrid-scale model[J]. International Journal for Numerical Methods in Fluids,2012,69(9): 1457-1472. doi: 10.1002/fld.2645
|
| [32] |
HUANG P G,COLEMAN G N. Van driest transformation and compressible wall-bounded flows[J]. AIAA Journal,1994,32(10): 2110-2113. doi: 10.2514/3.12259
|
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