Skip to main content
SpringerLink
Log in

Hybrid method based on embedded coupled simulation of vortex particles in grid based solution

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

The paper presents a novel hybrid approach developed to improve the resolution of concentrated vortices in computational fluid mechanics. The method is based on combination of a grid based and the grid free computational vortex (CVM) methods. The large scale flow structures are simulated on the grid whereas the concentrated structures are modeled using CVM. Due to this combination the advantages of both methods are strengthened whereas the disadvantages are diminished. The procedure of the separation of small concentrated vortices from the large scale ones is based on LES filtering idea. The flow dynamics is governed by two coupled transport equations taking two-way interaction between large and fine structures into account. The fine structures are mapped back to the grid if their size grows due to diffusion. Algorithmic aspects of the hybrid method are discussed. Advantages of the new approach are illustrated on some simple two dimensional canonical flows containing concentrated vortices.

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

Similar content being viewed by others

References

  1. Kornev N (2014) Improvement of vortex resolution through application of hybrid methods. In: Proceedings of the 6th international conference on vortex flows and vortex models (ICVFM Nagoya 2014), 17–20 Nov 2014, Nagoya

  2. Kornev N, Jacobi G (2013) Development of a hybrid approach using coupled grid-based and grid-free method. Proceedings Conference Marine 2013, Hamburg, paper 292

  3. Kornev N, Jacobi G (2013) Development of a hybrid grid- and particle-based numerical method for resolution of fine vortex structures in fluid mechanics. In: III international conference on particle-based method, fundamentals and applications (particles 2013), Stuttgart, pp 458–469

  4. Kornev N (2014) Increase of vortex resolution in computational fluid mechanics by a combination of grid- and particle-based methods. In: Proceedings of the 11th world congress on computational mechanics (WCCM XI), 22–25 July 2014, Barcelona

  5. Cottet GH, Koumotsakos P (2000) Vortex methods: theory and practice. Cambridge University Press, Cambridge

    Book  Google Scholar 

  6. Guermond JL, Huberson S, Shen WS (1993) Simulation of 2D external viscous flows by means of a domain decomposition method. J Comput Phys 108:343–352

    Article  MathSciNet  MATH  Google Scholar 

  7. Ould-Salihi ML, Cottet G-H, El Hamraoui M (2000) Blending finite-difference and vortex methods. SIAM J Sci Comput 22(5):1655–1674

    Article  MathSciNet  MATH  Google Scholar 

  8. Daeninck G (2006) Developments in hybrid approaches: vortex method with known separation location; vortex method with near-wall Eulerian solver; RANS-LES coupling. PhD thesis, Universite Catholique de Louvain, Belgium

  9. Stock MJ, Gharakhani A, Stone CP (2010) Modeling rotor wakes with a hybrid OVERFLOW-vortex method on a GPU cluster. In: 28th AIAA applied aerodynamics conference

  10. Winckelmans G, Chatelain P, Marichal Y, Parmentier P, Duponcheel M, Caprace D-G, Gillis T (2016) Recent developments in vortex particle-mesh (VPM) methods and applications. In: Proceedings of international conference on vortex flows and models 2016, Rostock

  11. Belotserkovsky SM, Kotovsky VN, Nisht MI, Fedorov RM (1988) Mathematical modeling of plane parallel separation flows. Nauka, Moscow (in Russian)

    Google Scholar 

  12. Voutsinas SG (2006) Vortex methods in aeronautics: how to make things work. Int J Comput Fluid Dyn 20(1):3–18

    Article  MathSciNet  MATH  Google Scholar 

  13. Wu JC (1976) Numerical boundary conditions for viscous flow problems. AIAAJ 14:1042–1049

    Article  MATH  Google Scholar 

  14. Koumoutsakos P, Leonard A, Pepin F (1994) Viscous boundary conditions for vortex methods. J Comput Phys 113:52–56

    Article  MathSciNet  MATH  Google Scholar 

  15. Coquerelle M, Cottet G-H (2008) A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies. J Comput Phys 227:9121–9137

    Article  MathSciNet  MATH  Google Scholar 

  16. Mimeau C, Cottet G-H, Mortazavi I (2016) A vortex penalization method for the simulation of 3D incompressible flows. In: Proceedings of international conference on vortex flows and models, Rostock

  17. Bernard PS, Collins P, Potts M (2005) Vortex method simulation of ground vehicle aerodynamics. SAE Transactions Journal of Passenger Cars: Mechanical Systems. SAE paper 2005-01-0549

  18. Kamemoto K (2008) Progressive application of a Lagrangian vortex method into fluid engineering and possibility of the concept of discrete element methods in vortex dynamics. In: Proceedings of 4th international conference on vortex flows and vortex models(ICVFM2008), 21–23 April 2008, Daejeon, pp 1–15

  19. Cottet G-H, Poncet P (2003) Advances in direct numerical simulations of 3D wall-bounded flows by vortex-in-cell methods. J Comput Phys 193(1):136–158

    Article  MathSciNet  MATH  Google Scholar 

  20. El Ossmani M, Poncet P (2010) Efficiency of multiscale hybrid grid-particle vortex methods. Multiscale Model Simul 8(5):1671–1690

    Article  MathSciNet  MATH  Google Scholar 

  21. Häckia C, Rebouxa S, Sbalzarinia IF (2015) A self-organizing adaptive-resolution particle method with anisotropic kernels. Procedia IUTAM 18:40–55

    Article  Google Scholar 

  22. Reboux S, Schrader B, Sbalzarini IF (2012) A self-organizing Lagrangian particle method for adaptive-resolution advectiondiffusion simulations. J Comput Phys 231:3623–3646

    Article  MathSciNet  MATH  Google Scholar 

  23. Koumoutsakos P (2005) Multiscale flow simulations using particles. Annu Rev Fluid Mech 37:457–487

    Article  MathSciNet  MATH  Google Scholar 

  24. Selle A, Rasmussen N, Fedkiw R (2005) A vortex particle method for smoke, water and explosions. ACM Trans Graph (TOG) 24(3):910–914

    Article  Google Scholar 

  25. Kornev N, Zhdanov V, Hassel E (2014) Experimental study of fine turbulent structures in a confined jet flow. In: 10th International ERCOFTAC symposium on engineering turbulence modelling and measurements (ETMM10), Marbella, 17–19 Sept 2014

  26. Chakraborty P, Balachandar S, Adrian RJ (2005) On the relationships between local vortex identification schemes. J Fluid Mech 535:189–214

    Article  MathSciNet  MATH  Google Scholar 

  27. Bagrinovskii KA, Godunov SK (1957) Difference schemes for multidimensional problems. Proc Acad Sci USSR (NS) 115:431–433

    MathSciNet  MATH  Google Scholar 

  28. Marchuk GI (1990) Splitting and alternating direction methods. In: Ciarlet PG, Lions JL (eds) Handbok on numerical analysis, vol I. Elsevier, North-Holland

    Google Scholar 

  29. Peaceman DW, Rachford HH (1955) The numerical solution of parabolic and elliptic differential equations. J Soc Ind Appl Math 3(1):28–41

    Article  MathSciNet  MATH  Google Scholar 

  30. Weinan E (2011) Principles of multiscale modeling. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  31. Vincent A, Meneguzzi M (1994) The dynamics of vorticity tubes in homogeneous turbulence. J Fluid Mech 258:245–254

    Article  MATH  Google Scholar 

  32. Vincent A, Meneguzzi M (1991) The spatial structure and statistical properties of homogeneous turbulence. J Fluid Mech 225:1–20

    Article  MATH  Google Scholar 

  33. Carlier J, Stanislas M (2005) Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J Fluid Mech 535:143–188

    Article  MathSciNet  MATH  Google Scholar 

  34. Atkinson C, Kitsios V, Sillero J, J Soria J (2014) On the organization of vortical structures in high Reynolds number turbulent boundary layers. In: 10th International ERCOFTAC symposium on engineering turbulence modelling and measurements (ETMM10), Marbella, 17–19 Sept 2014

  35. Greengard C (1985) The core spreading vortex method approximates the wrong equation. J Comput Phys 61:345–348

    Article  MathSciNet  MATH  Google Scholar 

  36. Seibold B (2008) A compact and fast Matlab code solving the incompressible Navier–Stokes equations on rectangular domains. http://www-math.mit.edu/~seibold

  37. Samarbakhsh S, Kornev N (2016) Hybrid method based on embedded coupled simulation of vortex particles in grid solution. In: Proceedings of international conference on vortex flows and models 2016, Rostock

  38. Pullin DI, Saffman PG (1994) Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence. Phys Fluids 6:1787–1796

    Article  MathSciNet  MATH  Google Scholar 

  39. Frick P (1999) Turbulence, models and methods. Lecture course, vol 2. Perm State University, Perm

    Google Scholar 

  40. Babiano A, Frick P, Dubrulle B (1995) Scaling properties of numerical two-dimensional turbulence. Phys Rev E 52(4):3719–3729

    Article  MATH  Google Scholar 

  41. Babiano A, Basdevant C, Legras B, Sadourny R (1987) Vorticity and passive-scalar dynamics in two-dimensional turbulence. J Fluid Mech 183:379–397

    Article  Google Scholar 

  42. Okuda H (1972) Nonphysical noises and instabilities in plasma simulation due to a spatial grid. J Comput Phys 10(3):475–486

    Article  Google Scholar 

Download references

Acknowledgements

The support of the author by the Japanese Society for Promotion of Science (JSPS) under Grant S-14062 and the German Research Foundation (Deutsche Forschungsgemeinschaft) under the Grants AB 112/10-1 and INST 264/113-1 FUGG is gratefully acknowledged.

Author information

Authors and Affiliations

  1. University of Rostock, A. Einstein Str., 2, 18059, Rostock, Germany

    Nikolai Kornev

Authors
  1. Nikolai Kornev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolai Kornev.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kornev, N. Hybrid method based on embedded coupled simulation of vortex particles in grid based solution. Comp. Part. Mech. 5, 269–283 (2018). https://doi.org/10.1007/s40571-017-0167-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-017-0167-2

Keywords

Mathematics Subject Classification

Search

Navigation