ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth TENO nonlinear weight
Received date: 2024-04-24
Revised date: 2024-05-13
Accepted date: 2024-07-09
Online published: 2024-08-05
Supported by
National Natural Science Foundation of China(52376114);National Science and Technology Major Project(2017-III-0005-0029)
The flow environment of spacecraft involves complex flow phenomena such as shock waves and turbulence. The coexistence of shock wave discontinuities and multiscale turbulent structures in the flow field poses significant challenges to high-order accurate numerical simulations. To effectively reduce numerical dissipation in turbulence simulations， a sixth-order central/fifth-order upwind linear hybrid interpolation was developed under the framework of Weighted Compact Nonlinear Scheme （WCNS）. Considering the high-resolution shock capturing characteristics， the scale separation strategy in the TENO scheme is used to develop nonlinear weight functions. For the numerical convergence of the numerical scheme， a smooth S-TENO nonlinear weight function is further developed. Through Approximate Dispersion Relations （ADR）， one-dimensional convection problems， and self-adaptive turbulence eddy simulation of three-dimensional channel， it was found that the linear stencil using a sixth-order central/fifth-order upwind linear hybrid interpolation stencil can significantly reduce the numerical dissipation of the scheme， thereby improving the prediction accuracy of channel flow and transonic flow past an airfoil. The proposed smooth S-TENO nonlinear weight not only maintains the good dispersion and dissipation properties of the original TENO nonlinear weight， but also significantly improves the numerical convergence in the cases of shock wave/turbulent boundary layer interaction when transonic flow past an airfoil， thus improving the accuracy of computational results. The numerical results indicate that the optimized sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth S-TENO weight can achieve both low numerical dissipation and good convergence， which is helpful to improve the accuracy of simulations in complex shock/turbulence problems.
Wenchang WU , Xingsi HAN , Yaobing MIN , Zhenguo YAN , Yankai MA . Sixth-order low-dissipation WCNS-CU6-ST scheme based on smooth TENO nonlinear weight[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(S1) : 730598 -730598 . DOI: 10.7527/S1000-6893.2024.30598
| 1 | LIU X D， OSHER S， CHAN T. Weighted essentially non-oscillatory schemes［J］. Journal of Computational Physics， 1994， 115（1）： 200-212. |
| 2 | JIANG G S， SHU C W. Efficient implementation of weighted ENO schemes［J］. Journal of Computational Physics， 1996， 126（1）： 202-228. |
| 3 | GEROLYMOS G A， SéNéCHAL D， VALLET I. Very-high-order WENO schemes［J］. Journal of Computational Physics， 2009， 228（23）： 8481-8524. |
| 4 | JOHNSEN E， LARSSON J， BHAGATWALA A V， et al. Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves［J］. Journal of Computational Physics， 2010， 229（4）： 1213-1237. |
| 5 | BORGES R， CARMONA M， COSTA B， et al. An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws［J］. Journal of Computational Physics， 2008， 227（6）： 3191-3211. |
| 6 | HENRICK A K， ASLAM T D， POWERS J M. Mapped weighted essentially non-oscillatory schemes： Achieving optimal order near critical points［J］. Journal of Computational Physics， 2005， 207（2）： 542-567. |
| 7 | ACKER F， DE R BORGES R B， COSTA B. An improved WENO-Z scheme［J］. Journal of Computational Physics， 2016， 313： 726-753. |
| 8 | LUO X， WU S P. An improved WENO-Z+ scheme for solving hyperbolic conservation laws［J］. Journal of Computational Physics， 2021， 445： 110608. |
| 9 | FAN P. High order weighted essentially nonoscillatory WENO-η schemes for hyperbolic conservation laws［J］. Journal of Computational Physics， 2014， 269： 355-385. |
| 10 | 刘博， 李诗尧， 陈嘉禹， 等. 基于映射函数的新型五阶WENO格式［J］. 航空学报， 2022， 43（12）： 126155. |
| LIU B， LI S Y， CHEN J Y， et al. New fifth order WENO scheme based on mapping functions［J］. Acta Aeronautica et Astronautica Sinica， 2022， 43（12）： 126155 （in Chinese）. | |
| 11 | LELE S K. Compact finite difference schemes with spectral-like resolution［J］. Journal of Computational Physics， 1992， 103（1）： 16-42. |
| 12 | DENG X G， ZHANG H X. Developing high-order weighted compact nonlinear schemes［J］. Journal of Computational Physics， 2000， 165（1）： 22-44. |
| 13 | DENG X G， MAEKAWA H. Compact high-order accurate nonlinear schemes［J］. Journal of Computational Physics， 1997， 130（1）： 77-91. |
| 14 | DENG X G， LIU X， MAO M L， et al. Investigation on weighted compact fifth-order nonlinear scheme and applications to complex flow［C］∥ Proceedings of the 17th AIAA Computational Fluid Dynamics Conference. Reston： AIAA， 2005. |
| 15 | DENG X G， MAO M L， TU G H， et al. Extending weighted compact nonlinear schemes to complex grids with characteristic-based interface conditions［J］. AIAA Journal， 2010， 48（12）： 2840-2851. |
| 16 | DENG X G， MIN Y B， MAO M L， et al. Further studies on Geometric Conservation Law and applications to high-order finite difference schemes with stationary grids［J］. Journal of Computational Physics， 2013， 239： 90-111. |
| 17 | 王运涛， 孙岩， 王光学， 等. DLR-F6翼身组合体的高阶精度数值模拟［J］. 航空学报， 2015， 36（9）： 2923-2929. |
| WANG Y T， SUN Y， WANG G X， et al. High-order accuracy numerical simulation of DLR-F6 wing-body configuration［J］. Acta Aeronautica et Astronautica Sinica， 2015， 36（9）： 2923-2929 （in Chinese）. | |
| 18 | 王运涛， 孙岩， 孟德虹， 等. CRM翼/身/平尾组合体模型高阶精度数值模拟［J］. 航空学报， 2016， 37（12）： 3692-3697. |
| WANG Y T， SUN Y， MENG D H， et al. High-order precision numerical simulation of CRM wing/body/horizontal tail model［J］. Acta Aeronautica et Astronautica Sinica， 2016， 37（12）： 3692-3697 （in Chinese）. | |
| 19 | NONOMURA T， FUJII K. Effects of difference scheme type in high-order weighted compact nonlinear schemes［J］. Journal of Computational Physics， 2009， 228（10）： 3533-3539. |
| 20 | FU L， HU X Y， ADAMS N A. A family of high-order targeted ENO schemes for compressible-fluid simulations［J］. Journal of Computational Physics， 2016， 305： 333-359. |
| 21 | HAMZEHLOO A， LUSHER D J， LAIZET S， et al. On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high-speed compressible flows［J］. International Journal for Numerical Methods in Fluids， 2021， 93（1）： 176-196. |
| 22 | DE VANNA F， BALDAN G， PICANO F， et al. Effect of convective schemes in wall-resolved and wall-modeled LES of compressible wall turbulence［J］. Computers & Fluids， 2023， 250： 105710. |
| 23 | FU L. Review of the high-order TENO schemes for compressible gas dynamics and turbulence［J］. Archives of Computational Methods in Engineering， 2023， 30（4）： 2493-2526. |
| 24 | HIEJIMA T. A high-order weighted compact nonlinear scheme for compressible flows［J］. Computers & Fluids， 2022， 232： 105199. |
| 25 | ZHANG H B， ZHANG F， XU C G. Towards optimal high-order compact schemes for simulating compressible flows［J］. Applied Mathematics and Computation， 2019， 355： 221-237. |
| 26 | ZHANG H B， ZHANG F， LIU J， et al. A simple extended compact nonlinear scheme with adaptive dissipation control［J］. Communications in Nonlinear Science and Numerical Simulation， 2020， 84： 105191. |
| 27 | 吴文昌， 马燕凯， 韩省思， 等. 一种光滑型 TENO非线性加权的WCNS格式 ［J］. 航空学报， 2024， 45 （8）： 129052. |
| WU W C， MA Y K， HAN X S， et al. A smooth TENO nonlinear weighting for WCNS scheme［J］. Acta Aeronautica et Astronuatica Sinica， 2024， 45 （8）： 129052 （in Chinese）. | |
| 28 | GARNIER E， MOSSI M， SAGAUT P， et al. On the use of shock-capturing schemes for large-eddy simulation［J］. Journal of Computational Physics， 1999， 153（2）： 273-311. |
| 29 | KAMIYA T， ASAHARA M， NONOMURA T. Application of central differencing and low-dissipation weights in a weighted compact nonlinear scheme［J］. International Journal for Numerical Methods in Fluids， 2017， 84（3）： 152-180. |
| 30 | HU X Y， WANG Q， ADAMS N A. An adaptive central-upwind weighted essentially non-oscillatory scheme［J］. Journal of Computational Physics， 2010， 229（23）： 8952-8965. |
| 31 | FAN P， SHEN Y Q， TIAN B L， et al. A new smoothness indicator for improving the weighted essentially non-oscillatory scheme［J］. Journal of Computational Physics， 2014， 269： 329-354. |
| 32 | WONG M L， LELE S K. High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows［J］. Journal of Computational Physics， 2017， 339： 179-209. |
| 33 | ZHAO G Y， SUN M B， XIE S B， et al. Numerical dissipation control in an adaptive WCNS with a new smoothness indicator［J］. Applied Mathematics and Computation， 2018， 330： 239-253. |
| 34 | PIROZZOLI S. On the spectral properties of shock-capturing schemes［J］. Journal of Computational Physics， 2006， 219（2）： 489-497. |
| 35 | 赵钟， 何磊， 何先耀. 风雷（PHengLEI）通用CFD软件设计［J］. 计算机工程与科学， 2020， 42（2）： 210-219. |
| ZHAO Z， HE L， HE X Y. Design of general CFD software PHengLEI［J］. Computer Engineering & Science， 2020， 42（2）： 210-219 （in Chinese）. | |
| 36 | HAN X S， KRAJNOVI? S. An efficient very large eddy simulation model for simulation of turbulent flow［J］. International Journal for Numerical Methods in Fluids， 2013， 71（11）： 1341-1360. |
| 37 | HAN X S， KRAJNOVI? S. Very-large-eddy simulation based on k-ω model［J］. AIAA Journal， 2015， 53（4）： 1103-1108. |
| 38 | HAN X S， KRAJNOVI? S. Validation of a novel very large eddy simulation method for simulation of turbulent separated flow［J］. International Journal for Numerical Methods in Fluids， 2013， 73（5）： 436-461. |
| 39 | MIN Y B， WU W C， ZHANG H D， et al. Self-adaptive turbulence eddy simulation of flow control for drag reduction around a square cylinder with an upstream rod［J］. European Journal of Mechanics-B/Fluids， 2023， 100： 185-201. |
| 40 | 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. |
| 41 | WU W C， HAN X S， MIN Y B， et al. Improved self-adaptive turbulence eddy simulation for complex flows and stall prediction using high-order schemes［J］. European Journal of Mechanics- B/Fluids， 2024， 106： 48-64. |
| 42 | JACQUIN L， MOLTON P， DECK S， et al. Experimental study of shock oscillation over a transonic supercritical profile［J］. AIAA Journal， 2009， 47（9）： 1985-1994. |
| 43 | CUONG NGUYEN N， TERRANA S， PERAIRE J. Large-eddy simulation of transonic buffet using matrix-free discontinuous Galerkin method［J］. AIAA Journal， 2022， 60（5）： 3060-3077. |
/
| 〈 |
|
〉 |
CJA