Skip to main content
SpringerLink
Log in

Effects of parallel strategies in the transitional flow investigation

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The direct numerical simulation of transitional and turbulent incompressible flows is an area that is increasing with the advance in computational resources. Code parallelization has became a useful tool in these simulations. In the present paper the unsteady two dimensional Navier–Stokes equations are used as physical model. Tollmien–Schlichting waves propagating in a Poiseuille flow is adopted as test case. Three frequencies showing different behavior according to the linear stability theory (LST) are used: unstable, nearly neutral and stable waves. The parallelization is done via domain decomposition in the streamwise direction. The time derivative is integrated by a classical fourth-order Runge–Kutta method. High-order compact finite difference schemes are used for the spatial derivatives discretization. The Poisson equation is solved by multigrid methods. The present paper explores different parallelization techniques for solving the tridiagonal system, and the multigrid method. The results are compared with LST, and also between the different parallel strategies to show the advantages and disadvantages of each one.

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Kim W, Menon S (1999) An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows. Int J Numer Method Fluids 31:983–1017

    Article  MATH  Google Scholar 

  2. Lele SK (1992) Compact finite difference schemes with spectral-like resolution. J Comput Phys 103:16–42. doi:10.1016/0021-9991(92)90324-R

    Article  MATH  MathSciNet  Google Scholar 

  3. Hirsh RS (1975) Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J Comput Phys 19(1):90–109. doi:10.1016/0021-9991(75)90118-7

    Article  MATH  MathSciNet  Google Scholar 

  4. Wray A, Hussaine MY (1994) Highly accurate compact methods and boundary conditions. Proc Royal soc Lond A392:373–389

    Google Scholar 

  5. Kloker MJ (1998) A robust high-resolution split-type compact FD-scheme for spatial direct numerical simulation of boundary-layer transition. Appl Sci Res 59(4):353–377. doi:10.1023/A:1001122829539

    Article  MATH  MathSciNet  Google Scholar 

  6. Mahesh K (1998) A family of high order finite difference schemes with good spectral resolution. J Comput Phys 145:332–358. doi:10.1006/jcph.1998.6022

    Article  MATH  MathSciNet  Google Scholar 

  7. de Souza LF, de Mendonça MT, de Medeiros MAF (2005) The advantages of using high-order finite differences schemes in laminar-turbulent transition studies. Int J Numer Methods Fluids 48:565–582. doi:10.1002/fld.955

    Article  MATH  Google Scholar 

  8. Zhang J (1996) Acceleration of five-point red-black Gauss–Seidel in multigrid for Poisson equation. Appl Math Comput 80:73–93. doi:10.1016/0096-3003(95)00276-6

    Article  MATH  MathSciNet  Google Scholar 

  9. Zhang J (1997) Residual scaling techniques in multigrid, I: equivalence proof. Appl Math Comput 86:283–303. doi:10.1016/S0096-3003(96)00194-4

    Article  MATH  MathSciNet  Google Scholar 

  10. Spitaleri RM (2000) Full-fas multigrid grid generation algorithms. Appl Numer Math 32:483–494. doi:10.1016/S0168-9274(99)00064-1

    Article  MATH  MathSciNet  Google Scholar 

  11. Gupta MM, Kouatchou J, Zhang J (1997) Comparison of second and fourth order discretizations for multigrid Poisson solvers. J Comput Phys 132:226–232. doi:10.1006/jcph.1996.5466

    Article  MATH  MathSciNet  Google Scholar 

  12. Velde EFV (1994) Concurrent scientific computing. Springer, New York

  13. Brandt A (1977) Multilevel adaptative solutions to boundary values problems. Math comput 31:333–390

    Article  MATH  Google Scholar 

  14. Huang Y, Guia U (1992) A multigrid method for solution of vorticity-velocity form of 3-D Navier–Stokes equations. Commun Appl Numer Methods 8:707–719

    Article  MATH  Google Scholar 

  15. Fish J, Pandheeradi M, Belsky V (1995) An efficient multilevel solution scheme for large scale non-linear systems. Int J Numer Methods Eng 38:1597–1610

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang J (2002) Multigrid method and fourth-order compact scheme for 2D Poisson equation with unequal mesh-size discretization. J Comput Phys 179:170–179

    Article  MATH  Google Scholar 

  17. Ge Y (2010) Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation. J Comput Phys 229:6381–6391

    Article  MATH  MathSciNet  Google Scholar 

  18. Henniger R, Obrist D, Kleiser L (2010) High-order accurate solution of the incompressible Navier–Stokes equations on massively parallel computers. J Comput Phys 229:3543–3572

    Article  MATH  MathSciNet  Google Scholar 

  19. Buckeridge S, Scheichl R (2010) Parallel geometric multigrid for global weather prediction. Numer Linear Algebra Appl 17:325–342

    MATH  MathSciNet  Google Scholar 

  20. John V, Tobiska L (2000) Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier–Stokes equations. Int J Numer Methods Fluids 33:453–473

    Article  MATH  Google Scholar 

  21. Fasel HF, Rist U, Konzelmann U (1990) Numerical investigation of the three-dimensional development in boundary-layer transition. AIAA J 28:29–37. doi:10.2514/3.10349

    Article  MathSciNet  Google Scholar 

  22. Souza LFd (2003) Instabilidade centrífuga e transição para turbulência em escoamentos laminares sobre superfícies côncavas. Ph.D. thesis, Instituto Tecnológico de Aeronáutica

Download references

Acknowledgments

The authors acknowledge the financial support received from FAPESP under grants 2009/03208-6, 2010/00880-2, 2011/08010-0 and 2013/00553-0.

Author information

Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação-ICMC, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

    J. K. Rogenski, L. A. Petri & L. F. de Souza

Authors
  1. J. K. Rogenski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. A. Petri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. F. de Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. F. de Souza.

Additional information

Technical Editor: Francisco Ricardo Cunha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rogenski, J.K., Petri, L.A. & de Souza, L.F. Effects of parallel strategies in the transitional flow investigation. J Braz. Soc. Mech. Sci. Eng. 37, 861–872 (2015). https://doi.org/10.1007/s40430-014-0221-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-014-0221-4

Keywords

Search

Navigation