Skip to main content
SpringerLink
Log in

Vortex methods for incompressible flow simulations on the GPU

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We present a remeshed vortex particle method for incompressible flow simulations on GPUs. The particles are convected in a Lagrangian frame and are periodically reinitialized on a regular grid. The grid is used in addition to solve for the velocity–vorticity Poisson equation and for the computation of the diffusion operators. In the present GPU implementation of particle methods, the remeshing and the solution of the Poisson equation rely on fast and efficient mesh-particle interpolations. We demonstrate that particle remeshing introduces minimal artificial dissipation, enables a faster computation of differential operators on particles over grid-free techniques and can be efficiently implemented on GPUs. The results demonstrate that, contrary to common practice in particle simulations, it is necessary to remesh the (vortex) particle locations in order to solve accurately the equations they discretize, without compromising the speed of the method. The present method leads to simulations of incompressible vortical flows on GPUs with unprecedented accuracy and efficiency.

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

Similar content being viewed by others

References

  1. Amada, T., Imura, M., Yasumuro, Y., Manabe, Y., Chihara, K.: Particle-based fluid simulation on GPU. In: ACM Workshop on General-Purpose Computing on Graphics Processors and SIGGRAPH 2004. Los Angeles, CA (2004)

  2. Bergdorf, M., Koumoutsakos, P.: A Lagrangian particle-wavelet method. Multiscale Model. Simul. 5(3), 980–995 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Briggs, W.L., Henson, V.E., McCormick, S.F.: A Multigrid Tutorial: Second Edition. SIAM, Philadelphia, PA (2000)

    MATH  Google Scholar 

  4. Chaniotis, A.K., Poulikakos, D., Koumoutsakos, P.: Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows. J. Comput. Phys. 182(1), 67–90 (2002)

    Article  MATH  Google Scholar 

  5. Cottet, G.H., Koumoutsakos, P.: Vortex Methods, Theory and Practice. Cambridge University Press (2000)

  6. Cottet, G.H., Maitre, E.: A level set method for fluid-structure interactions with immersed surfaces. Math. Models Methods Appl. Sci. 16(3), 415–438 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Foster, N., Metaxas, D.: Controlling fluid animation. In: Proceedings CGI ’97, pp. 178–188 (1997)

  8. Georgii, J., Westermann, R.: Mass-spring systems on the GPU. Simul. Model. Pract. Theory 13(8), 693–702 (2005)

    Article  Google Scholar 

  9. Hagen, T.R., Lie, K.A., Natvig, J.R.: Solving the Euler equations on graphics processing units. Comput. Sci. (ICCS 2006) 3994, 220–227 (2006)

    Article  Google Scholar 

  10. Harada, T., Koshizuka, S., Kawaguchi, Y.: Smoothed particle hydrodynamics on GPUs. In: Proc. of Computer Graphics International, pp. 63–70 (2007)

  11. Harris, M.J.: Fast fluid dynamics simulation on the GPU. In: GPU Gems: Programming Techniques, Tips, and Tricks for Real-Time Graphics, pp. 637–665. Addison-Wesley (2004)

  12. Kolb, A., Cuntz, N.: Dynamic particle coupling for GPU-based fluid simulation. In: Proc. ASIM, pp. 722–727 (2005)

  13. Kolb, A., Latta, L., Rezk-Salama, C.: Hardware-based simulation and collision detection for large particle systems. In: Proc. Graphics Hardware, pp. 123–131. ACM/Eurographics, Grenoble, France (2004)

    Google Scholar 

  14. Koumoutsakos, P.: Inviscid axisymmetrization of an elliptical vortex. J. Comput. Phys. 138(2), 821–857 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. Krüger, J., Schiwietz, T., Kipfer, P., Westermann, R.: Numerical simulations on PC graphics hardware. In: ParSim 2004 (Special Session of EuroPVM/MPI 2004) (2004)

  17. Hegeman, K., Carr, N.A., Miller, G.S.: Particle-based fluid simulation on the GPU. In: Computational Science – ICCS 2006, vol. 3994, pp. 228–235. Springer, Berlin/Heidelberg (2006)

    Chapter  Google Scholar 

  18. Minion, M.L., Brown, D.L.: Performance of under-resolved two-dimensional incompressible flow simulations, ii. J. Comput. Phys. 138, 734–765 (1997)

    Article  MATH  Google Scholar 

  19. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(8), 1703–1759 (2005)

    Article  MathSciNet  Google Scholar 

  20. Müller, M., Charypar, D., Gross, M.: Particle-based fluid simulation for interactive applications. In: SCA ’03: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 154–159. Eurographics Association, San Diego, CA (2003)

    Google Scholar 

  21. Pfister, H., Gross, M.: Point-based computer graphics. IEEE Comput. Graph. Appl. 24(4), 22–23 (2004)

    Article  Google Scholar 

  22. Scheidegger, C.E., Comba, J.L.D., da Cunha, R.D.: Practical CFD simulations on programmable graphics hardware using smac. Comput. Graph. Forum 24(4), 715–728 (2005)

    Article  Google Scholar 

  23. Selle, A., Rasmussen, N., Fedkiw, R.: A vortex particle method for smoke, water and explosions. ACM Trans. Graph. 24(3), 910–914 (2005). http://doi.acm.org/10.1145/1073204.1073282

    Article  Google Scholar 

  24. Stam, J.: A simple fluid solver based on the FFT. J. Graph. Tools 6(2), 43–52 (2001)

    MATH  Google Scholar 

  25. Treuille, A., Lewis, A., Popovic, Z.: Model reduction for real-time fluids. ACM Trans. Graph. 25(3), 826–834 (2006)

    Article  Google Scholar 

  26. Wu, E.H., Zhu, H.B., Liu, X.H., Liu, Y.Q.: Simulation and interaction of fluid dynamics. Visual Comput. 23(5), 299–308 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair of Computational Science, ETH Zurich, CH-8092, Zurich, Switzerland

    Diego Rossinelli & Petros Koumoutsakos

Authors
  1. Diego Rossinelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Petros Koumoutsakos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petros Koumoutsakos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rossinelli, D., Koumoutsakos, P. Vortex methods for incompressible flow simulations on the GPU. Visual Comput 24, 699–708 (2008). https://doi.org/10.1007/s00371-008-0250-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-008-0250-z

Keywords

Search

Navigation