Skip to main content
SpringerLink
Log in

Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers

适用于宽速域湍流流动的新型混合对称超松弛隐式时间格式评估

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The convergent efficiency and numerical stability of temporal discretization schemes for Navier-Stokes (N-S) equations are significant for engineering turbulent flow simulations. Through analysis of the original scalar and matrix versions of the symmetric successive over relaxation (SSOR) implicit temporal schemes, a novel scalar-matrix hybrid-SSOR scheme based on the local Mach number, which combines the advantages of both the scalar and matrix SSOR, is proposed and implemented in several flow simulations from low to hypersonic speeds. According to the results, the new hybrid-SSOR presents a few advantages and shows the best convergent performance for turbulent flows across a wide range of Mach numbers, mainly because of its high efficiency and excellent numerical stability. The hybrid-SSOR is expected to be widely implemented in engineering flow simulations.

摘要

N-S方程的时间离散格式的收敛效率和数值稳定性对工程湍流计算的意义十分重要. 通过对原始标量型和矩阵型对称超松弛隐式时间格式的分析, 提出了一种基于当地马赫数的混合型对称超松弛隐式时间格式. 该格式兼顾了标量型和矩阵型对称超松弛格式的优点, 被应用于从低速到高超声速的多个湍流流动的计算. 通过计算结果的对比表明, 新的混合型对称超松弛格式在较宽速域的湍流流动模拟中, 由于其高的计算效率和优异的数值稳定性, 表现出了最好的收敛特性. 该新型混合对称超松弛格式将有望广泛应用于工程湍流流动的计算.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. H. Luo, J. D. Baum, and R. Löhner, A fast, matrix-free implicit method for compressible flows on unstructured grids, J. Comput. Phys. 146, 664 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  2. R. F. Chen, and Z. J. Wang, Fast, block lower-upper symmetric gauss-seidel scheme for arbitrary grids, AIAA J. 38, 2238 (2000).

    Article  Google Scholar 

  3. G. Wang, Y. Jiang, and Z. Ye, An improved LU-SGS implicit scheme for high Reynolds number flow computations on hybrid unstructured mesh, Chin. J. Aeronaut. 25, 33 (2012).

    Article  Google Scholar 

  4. C. Gong, W. Bao, J. Liu, G. Tang, and Y. Jiang, An efficient wavefront parallel algorithm for structured three dimensional LU-SGS, Comput. Fluids 134–135, 23 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  5. Z. Ye, X. Wang, Z. Chen, and L. Wang, Unsteady aerodynamic characteristics of a horizontal wind turbine under yaw and dynamic yawing, Acta Mech. Sin. 36, 320 (2020).

    Article  MathSciNet  Google Scholar 

  6. Y. Long, X. Long, and B. Ji, LES investigation of cavitating flows around a sphere with special emphasis on the cavitation-vortex interactions, Acta Mech. Sin. 36, 1238 (2020).

    Article  MathSciNet  Google Scholar 

  7. A. Jameson, W. Schmidt, and E. Turkel, Numerical solutions of euler equations by finite volume methods with Runge-Kutta time stepping schemes, AIAA Paper No. 81-1259, 1981.

  8. Swanson R C, and Turkel E, A multistage time-stepping scheme for the Navier-Stokes equations, AIAA Paper No. 85-0035, 1985.

  9. R. M. Beam, and R. F. Warming, An implicit factored scheme for the compressible Navier-Stokes equations, AIAA J. 16, 393 (1978).

    Article  MATH  Google Scholar 

  10. S. Yoon, and A. Jameson, A lower-upper symmetric Gauss-Seidel method for the Euler and Navier-Stokes equations, AIAA J. 26, 1025 (1988).

    Article  Google Scholar 

  11. V. Venkatakrishnan, Implicit schemes and parallel computing in unstructured grid CFD, Comput. Fluid Dyn. 1995.

  12. A. Jameson, Time dependent calculations using multigrid with application to unsteady flows past airfoils and wings, AIAA paper No. 91-1596, 1991.

  13. A. Jameson, and S. Yoon, Lower-upper implicit schemes with multiple grids for the Euler equations, AIAA J. 25, 929 (1987).

    Article  Google Scholar 

  14. W. R. Briley, S. S. Neerarambam, and D. L. Whitfield, Implicit lower-upper/approximate-factorization schemes for incompressible flows, J. Comput. Phys. 128, 32 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Sharov, and K. Nakahashi, Low speed preconditioning and LU-SGS scheme for 3-D viscous flow computations on unstructured grids, AIAA paper No. 98-0614, 1998.

  16. G. Wang, H. H. Mian, Y. Liu, and Z. Ye, A hybrid implicit scheme for solving Navier-Stokes equations, Int. J. Numer. Meth. Fluids 78, 319 (2015).

    Article  MathSciNet  Google Scholar 

  17. L. Mottura, L. Vigevano, and M. Zaccanti, Factorized implicit upwind methods applied to inviscid flows at high mach number, AIAA J. 38, 1846 (2000).

    Article  Google Scholar 

  18. P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43, 357 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Liu, Z. Xiao, and S. Fu, Unsteady transition studies over a pitching airfoil using a k-ω-γ transition model, AIAA J. 56, 3776 (2018).

    Article  Google Scholar 

  20. J. Liu, W. Zhu, Z. Xiao, H. Sun, Y. Huang, and Z. Liu, DDES with adaptive coefficient for stalled flows past a wind turbine airfoil, Energy 161, 846 (2018).

    Article  Google Scholar 

  21. J. Liu, and Z. Xiao, Low-frequency oscillation over NACA0015 airfoil near stall at high Reynolds number, AIAA J. 58, 53 (2020).

    Article  Google Scholar 

  22. J. Liu, J. Chen, H. Ren, Y. Zhang, X. He, and Z. Xiao, Correlations of unsteady vortex burst point and dynamic stability over a pitching double-delta wing, Aerosp. Sci. Tech. 107, 106256 (2020).

    Article  Google Scholar 

  23. H. C. Lin, Dissipation additions to flux-difference splitting, J. Comput. Phys. 117, 20 (1995).

    Article  MATH  Google Scholar 

  24. B. Van Leer, Towards the Ultimate conservation difference scheme V: A second-order sequal to Godunov’s method, J. Comput. Phys. 32, 101 (1979).

    Article  MATH  Google Scholar 

  25. J. N. Scott, and Y. Y. Niu, Comparison of limiters in flux-split algorithms for Euler equations, AIAA paper No. 93-0068, 1993.

  26. F. R. Menter, M. Kuntz, and R. Langtry, in Ten years of experience with the SST turbulence model: Proceedings of 4th International Symposium on Turbulence Heat and Mass Transfer, 2003.

  27. P. R. Spalart, and S. R. Allmaras, A one-equation turbulence model for aerodynamic flows, AIAA paper No. 1992-0439, 1992.

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11902334, 91952302, and 91852113) and the National Numerical Wind Tunnel Project. The authors would also like to thank the National Key Research and Development Program of China (Grant No. 2019YFA0405300) and the National Key Project (Grant No. GJXM92579).

Author information

Authors and Affiliations

  1. State Key Laboratory of Aerodynamics, Mianyang, 621000, China

    Jian Liu  (刘健), Jianqiang Chen  (陈坚强) & Zipei Zhang  (张子佩)

  2. China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Jian Liu  (刘健), Jianqiang Chen  (陈坚强), Zipei Zhang  (张子佩) & Yufeng Yang  (杨玉峰)

  3. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Zhixiang Xiao  (肖志祥)

Authors
  1. Jian Liu  (刘健)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianqiang Chen  (陈坚强)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zipei Zhang  (张子佩)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yufeng Yang  (杨玉峰)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhixiang Xiao  (肖志祥)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhixiang Xiao  (肖志祥).

Additional information

Author contributions

Jian Liu proposed the Hybrid-SSOR scheme and wrote the most content of the article. Jianqiang Chen analyzed the computational results and provided several useful advices for the improvements of the Hybrid-SSOR scheme. Yufeng Yang implemented the temporal schemes, such as matrix-SSOR and Hybrid-SSOR, into the computational code. Zipei Zhang generated the computational grids and computed all the cases. Zhixiang Xiao organized the manuscript and revised the revisions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Chen, J., Zhang, Z. et al. Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers. Acta Mech. Sin. 39, 322398 (2023). https://doi.org/10.1007/s10409-022-22398-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-022-22398-x

Keywords

Search

Navigation