Skip to main content
SpringerLink
Log in

Simulation of the Laminar–Turbulent Transition by Applying Hybrid Difference Schemes

  • MATHEMATICAL PHYSICS
  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A simple hybrid difference scheme applicable to shock wave flows is proposed. The scheme remains monotone near shock waves and switches to a low-dissipative nonmonotone difference scheme in smooth flow regions, thus controlling the amount of numerical dissipation. This is achieved by smoothly decreasing a monotonizing correction term down to the prescribed threshold value depending on an indicator of solution smoothness. As an example, the laminar–turbulent transition in a supersonic boundary layer over a flat plate at a Mach number of 3 is simulated. The numerical results are compared with those of other works based on dissipative and low-dissipative schemes. More specifically, we compare the spectral characteristics of disturbances in the linear and nonlinear development domains, the transient flow structure, and averaged boundary layer characteristics.

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

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.

Similar content being viewed by others

REFERENCES

  1. I. V. Egorov, N. C. Nguyen, T. S. Nguyen, and P. V. Chuvakhov, “Simulation of the laminar–turbulent transition by applying dissipative numerical schemes,” Comput. Math. Math. Phys. 61 (2), 254–266 (2021).

    Article  MathSciNet  Google Scholar 

  2. C. S. J. Mayer, D. A. V. Terzi, and H. F. Fasel, “DNS of complete transition to turbulence via oblique breakdown at Mach 3,” AIAA Paper No. 2008-4398 (2008).

  3. I. V. Egorov and A. V. Novikov, “Direct numerical simulation of laminar–turbulent flow over a flat plate at hypersonic flow speeds,” Comput. Math. Math. Phys. 56 (6), 1048–1064 (2016).

    Article  MathSciNet  Google Scholar 

  4. F. Ducros, et al., “Large-eddy simulation of the shock/turbulence interaction,” J. Comput. Phys. 152 (2), 517–549 (1999).

    Article  Google Scholar 

  5. T. Kh. Karimov, “On some iteration methods for solving nonlinear equations in Hilbert spaces,” Dokl. Akad. Nauk SSSR 269 (5), 1038–1046 (1983).

    MathSciNet  Google Scholar 

  6. P. V. Chuvakhov, A. V. Fedorov, and A. O. Obraz, “Numerical simulation of turbulent spots generated by unstable wave packets in a hypersonic boundary layer,” Comput. Fluids 162, 26–38 (2018). https://doi.org/10.1016/j.compfluid.2017.12.001

    Article  MathSciNet  MATH  Google Scholar 

  7. F. M. White, Viscous Fluid Flow (McGraw-Hill, New York, 1991).

    Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation (project no. 21-19-00307) and was performed at the Moscow Institute of Physics and Technology with the use of computing resources of the federal collective use center Complex for Simulation and Data Processing for Mega-science Facilities at NRC “Kurchatov Institute,” http://ckp.nrcki.ru/.

Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    I. V. Egorov & N. C. Nguyen

  2. Central Aerohydrodynamic Institute (TsAGI), National Research Center “Zhukovsky Institute”, 140180, Zhukovskii, Moscow oblast, Russia

    I. V. Egorov

Authors
  1. I. V. Egorov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. C. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. C. Nguyen.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Egorov, I.V., Nguyen, N.C. Simulation of the Laminar–Turbulent Transition by Applying Hybrid Difference Schemes. Comput. Math. and Math. Phys. 62, 658–673 (2022). https://doi.org/10.1134/S0965542522040054

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542522040054

Keywords:

Search

Navigation