Skip to main content
SpringerLink
Log in

Visual simulation of turbulent fluids using MLS interpolation profiles

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

Abstract

A detailed description of turbulent fluids based on numerical simulation is an important research topic required by many visual effects. We propose a novel method to simulate fluids with turbulent small-scale details. By inserting diffusive derivatives and divergence-free constraints to moving least-squares (MLS) fitting, we upgrade the velocity interpolation method for existing fluid solvers to enhance the subgrid accuracy. The time-step restriction of asymptotic property of diffusive derivatives is resolved by means of coupling to the constrained interpolation profile (CIP) advection framework. The proposed constrained moving least-squares interpolation profile (CMIP) method provides intuitive control over turbulence through the adjustment of one parameter as though controlling the Reynolds number with an inviscid model. The proposed method generates improved visuals of the highly turbulent fluid and is complementary to existing techniques that are currently being used.

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

Similar content being viewed by others

References

  1. Bridson, R., Houriham, J., Nordenstam, M.: Curl-noise for procedural fluid flow. ACM Trans. Graph. 26(3), 46 (2007). SIGGRAPH Proc.

    Article  Google Scholar 

  2. Chorin, A.: A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2, 12–26 (1967)

    Article  MATH  Google Scholar 

  3. Fedkiw, R., Stam, J., Jensen, H.: Visual simulation of smoke. In: Proc. of SIGGRAPH 01, pp. 15–22 (2001)

    Google Scholar 

  4. Feldman, B., O’Brien, J., Klingner, B.: Animating gases with hybrid meshes. ACM Trans. Graph. 24(3), 904–909 (2005). SIGGRAPH Proc.

    Article  Google Scholar 

  5. Foster, N., Metaxas, D.: Realistic animation of liquids. Graph. Models Image Process. 58, 471–483 (1996)

    Article  Google Scholar 

  6. Foster, N., Metaxas, D.: Modeling the motion of a hot, turbulent gas. In: Proc. of SIGGRAPH ’97, pp. 181–188 (1997)

    Google Scholar 

  7. Fresch, U.: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  8. Gao, Y., Li, C.F., Hu, S.M., Barsky, B.A.: Simulating gaseous fluids with low and high speeds. Comput. Graph. Forum 28(7), 1845–1852 (2009). Proc. Pacific Graphics, 2009

    Article  Google Scholar 

  9. Greenwood, S.T., House, D.H.: Better with bubbles: enhancing the visual realism of simulated fluid. In: Proc. of the 2004 ACM SIGGRAPH/Eurographics Symp. on Comput. Animat., pp. 287–296 (2004)

    Chapter  Google Scholar 

  10. Hong, J.M., Kim, C.H.: Discontinuous fluids. ACM Trans. Graph. 24(3), 915–920 (2005). SIGGRAPH Proc.

    Article  Google Scholar 

  11. Hong, J.M., Shinar, T., Fedkiw, R.: Wrinkled flames and cellular patterns. ACM Trans. Graph. 26(3), 471–476 (2007). SIGGRAPH Proc.

    Article  Google Scholar 

  12. Hong, J.M., Lee, H.Y., Yoon, J.C., Kim, C.H.: Bubbles alive. ACM Trans. Graph. 27(3), 481–484 (2008). SIGGRAPH Proc.

    Article  Google Scholar 

  13. Hong, J.M., Yoon, Y.C., Kim, C.H.: Divergence-constrained moving least squares for fluid simulation. Comput. Animat. Virtual Worlds 19(3–4), 469–477 (2008). CASA Proc.

    Article  Google Scholar 

  14. Huerta, A., Vidal, Y., Villon, P.: Pseudo-divergence-free element free Galerkin method for incompressible fluid flow. Comput. Methods Appl. Mech. Eng. 193, 1119–1136 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, J., Cha, D., Chang, B., Koo, B., Ihm, I.: Practical animation of turbulent splashing water. In: Proc. of the 2006 ACM SIGGRAPH/Eurographics Symp. on Comput. Animat., pp. 335–344 (2006)

    Google Scholar 

  16. Kim, B., Liu, Y., Llamas, I., Rossignac, J.: Advections with significantly reduced dissipation and diffusion. IEEE Trans. Vis. Comput. Graph. 13, 135–144 (2007)

    Article  Google Scholar 

  17. Kim, D., Song, O., Ko, H.S.: A semi-Lagrangian CIP fluid solver without dimensional splitting. Comput. Graph. Forum 27(2), 467–475 (2008). Proc. Eurographics

    Article  Google Scholar 

  18. Kim, T., Thurey, N., James, D., Gross, M.: Wavelet turbulence for fluid simulation. ACM Trans. Graph. 27(3), 50 (2008). SIGGRAPH Proc.

    Article  Google Scholar 

  19. Kim, D., Song, O.Y., Ko, H.S.: Stretching and wiggling liquids. ACM Trans. Graph. 28(5), 120 (2009)

    Google Scholar 

  20. Lentine, M., Zheng, W., Fedkiw, R.: A novel algorithm for incompressible flow using only a coarse grid projection. ACM Trans. Graph. 29, 114:1–114:9 (2010)

    Article  Google Scholar 

  21. Lorenz, E.N.: The Essence of Chaos. University of Washington Press, Seattle (1996)

    Google Scholar 

  22. Losasso, F., Talton, J., Kwatra, N., Fedkiw, R.: Two-way coupled SPH and particle level set fluid simulation. IEEE Trans. Vis. Comput. Graph. 14(4), 797–804 (2008)

    Article  Google Scholar 

  23. Narain, R., Sewall, J., Carlson, M., Lin, M.: Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans. Graph. 27(5), 166 (2008). SIGGRAPH Asia Proc.

    Article  Google Scholar 

  24. Nayroles, B., Touzot, G., Villon, P.: Generalizing the finite element method: diffuse approximation and diffuse elements. Comput. Mech. 10, 307–318 (1992)

    Article  MATH  Google Scholar 

  25. Nealen, A.: An as-short-as possible introduction to the least squares, weighted least squares and moving least squares methods for scattered data approximation and interpolation. Tech. rep., TU Darmstadt (2004)

  26. Nguyen, D., Fedkiw, R., Jensen, H.: Physically based modeling and animation of fire. ACM Trans. Graph. 29, 721–728 (2002). SIGGRAPH Proc.

    Google Scholar 

  27. Pfaff, T., Thuerey, N., Gross, M.: Lagrangian vortex sheets for animating fluids. ACM SIGGRAPH 2012 Papers (2012)

  28. Schechter, H., Bridson, R.: Evolving sub-grid turbulence for smoke animation. In: Proc. of the 2008 ACM/Eurographics Symp. on Comput. Animat. (2008)

    Google Scholar 

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

    Article  Google Scholar 

  30. Selle, A., Fedkiw, R., Kim, B.M., Liu, Y., Rossignac, J.: An unconditionally stable MacCormack method. J. Sci. Comput. 35, 350–371 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  31. Shen, C., O’Brien, J.F., Shewchuk, J.: Interpolating and approximating implicit surfaces from polygon soup. ACM Trans. Graph. 31, 321–328 (2004). SIGGRAPH Proc.

    Google Scholar 

  32. Song, O., Shin, H., Ko, H.S.: Stable but non-dissipative water. ACM Trans. Graph. 24(1), 81–97 (2005)

    Article  Google Scholar 

  33. Stam, J.: Stable fluids. In: Proc. of SIGGRAPH 99, pp. 121–128 (1999)

    Google Scholar 

  34. Thuerey, N., Sadlo, F., Schirm, S., Muller-Fischer, M., Gross, M.: Real-time simulations of bubbles and foam within a shallow water framework. In: Proc. of the 2007 ACM SIGGRAPH/Eurographics Symp. on Comput. Animat., pp. 191–198 (2007)

    Google Scholar 

  35. Yabe, T., Aoki, T.: A universal solver for hyperbolic equations by cubic-polynomial interpolation I. One-dimensional solver. Comput. Phys. Commun. 66(2–3), 219–232 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  36. Yabe, T., Ishikawa, T., Wang, P.Y., Aoki, T., Kadota, Y., Ikeda, F.: A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers. Comput. Phys. Commun. 66(2–3), 233–242 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This Research is supported by Ministry of Culture, Sports and Tourism (MCST) and Korea Creative Content Agency (KOCCA) in the Culture Technology (CT) Research & Development Program 2012.

Author information

Authors and Affiliations

  1. Dongguk University—Seoul, 30 Pildong-ro 1-gil (26 Pildong-3), Jung-gu, Seoul, 100-715, Korea

    Sun-Tae Kim & Jeong-Mo Hong

Authors
  1. Sun-Tae Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeong-Mo Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeong-Mo Hong.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(MPG 31.4 MB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, ST., Hong, JM. Visual simulation of turbulent fluids using MLS interpolation profiles. Vis Comput 29, 1293–1302 (2013). https://doi.org/10.1007/s00371-012-0770-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-012-0770-4

Keywords

Search

Navigation