“A two-continua approach to Eulerian simulation of water spray” by Nielsen and Østerby

  • ©Michael B. Nielsen and Ole Østerby

Conference:


Type:


Title:

    A two-continua approach to Eulerian simulation of water spray

Session/Category Title: Voxels & Liquids


Presenter(s)/Author(s):


Moderator(s):



Abstract:


    Physics based simulation of the dynamics of water spray – water droplets dispersed in air – is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry and often challenge state of the art methods. Current spray simulation pipelines typically employ a combination of Lagrangian (particle) and Eulerian (volumetric) methods – the Eulerian methods being used for parts of the spray where individual droplets are not apparent. However, existing Eulerian methods in computer graphics are based on gas solvers that will for example exhibit hydrostatic equilibrium in certain scenarios where the air is expected to rise and the water droplets fall. To overcome this problem, we propose to simulate spray in the Eulerian domain as a two-way coupled two-continua of air and water phases co-existing at each point in space. The fundamental equations originate in applied physics and we present a number of contributions that make Eulerian two-continua spray simulation feasible for computer graphics applications. The contributions include a Poisson equation that fits into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods.

References:


    1. Angot, P., Bruneau, C.-H., and Fabrie, P. 1999. A penalization method to take into account obstacles in incompressible viscous flows. Numerische Mathematik 81, 4 (Feb.), 497–520.Google ScholarCross Ref
    2. Bao, K., Wu, X., Zhang, H., and Wu, E. 2010. Volume fraction based miscible and immiscible fluid animation. Comput. Animat. Virtual Worlds 21, 34 (May), 401–410. Google ScholarDigital Library
    3. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. In ACM SIGGRAPH 2007 papers, ACM, New York, SIGGRAPH ’07. Google ScholarDigital Library
    4. Brennen, C. 2009. Fundamentals of Multiphase Flow. Cambridge University Press.Google Scholar
    5. Bridson, R. 2008. Fluid Simulation for Computer Graphics. AK Peters. Google ScholarDigital Library
    6. Briggs, W. L., Henson, V. E., and McCormick, S. F. 2000. A multigrid tutorial (2nd ed.). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA. Google ScholarDigital Library
    7. Chentanez, N., and Müller, M. 2010. Real-time simulation of large bodies of water with small scale details. In Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Eurographics Association, Aire-la-Ville, Switzerland, SCA ’10, 197–206. Google ScholarDigital Library
    8. Coddington, E. A. 1989. An Introduction to Ordinary Differential Equations. Dover Books on Advanced Mathematics. Dover Publ.Google Scholar
    9. Dupont, T. F., and Liu, Y. 2007. Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations. Math. Comput. 76, 258, 647–668.Google Scholar
    10. Fedkiw, R., Stam, J., and Jensen, H. W. 2001. Visual simulation of smoke. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, New York, SIGGRAPH ’01, 15–22. Google ScholarDigital Library
    11. Fournier, A., and Reeves, W. T. 1986. A simple model of ocean waves. SIGGRAPH Comput. Graph. 20, 4 (Aug.), 75–84. Google ScholarDigital Library
    12. Froemling, E., Goktekin, T., and Peachey, D. 2007. Simulating whitewater rapids in ratatouille. In ACM SIGGRAPH 2007 sketches, ACM, New York, SIGGRAPH ’07. Google ScholarDigital Library
    13. Geiger, W., Leo, M., Rasmussen, N., Losasso, F., and Fedkiw, R. 2006. So real it’ll make you wet. In ACM SIGGRAPH 2006 Sketches, ACM, New York, SIGGRAPH ’06. Google ScholarDigital Library
    14. Huang, C.-S., Arbogast, T., and Qiu, J. 2012. An eulerian-lagrangian weno finite volume scheme for advection problems. J. Comput. Phys. 231, 11 (June), 4028–4052. Google ScholarDigital Library
    15. Ihmsen, M., Akinci, N., Akinci, G., and Teschner, M. 2012. Unified spray, foam and air bubbles for particle-based fluids. The Visual Computer 28 (Apr.), 669–677. Google ScholarDigital Library
    16. Integrator, 2013. http://integrals.wolfram.com.Google Scholar
    17. Jiang, G.-S., and Peng, D. 1999. Weighted eno schemes for hamilton–jacobi equations. SIAM J. Sci. Comput. 21, 6 (Dec.), 2126–2143. Google ScholarDigital Library
    18. Kang, N., Park, J., yong Noh, J., and Shin, S. Y. 2010. A hybrid approach to multiple fluid simulation using volume fractions. Comput. Graph. Forum 29, 2, 685–694.Google ScholarCross Ref
    19. Kim, J., Cha, D., Chang, B., Koo, B., and Ihm, I. 2006. Practical animation of turbulent splashing water. In Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, Aire-la-Ville, Switzerland, SCA ’06, 335–344. Google ScholarDigital Library
    20. Lentine, M., Grétarsson, J. T., and Fedkiw, R. 2011. An unconditionally stable fully conservative semi-lagrangian method. J. Comput. Phys. 230, 8 (Apr.), 2857–2879. Google ScholarDigital Library
    21. Liu, S., Wang, Z., Gong, Z., and Peng, Q. 2008. Simulation of atmospheric binary mixtures based on two-fluid model. Graph. Models 70, 6 (Nov.), 117–124. Google ScholarDigital Library
    22. Losasso, F., Shinar, T., Selle, A., and Fedkiw, R. 2006. Multiple interacting liquids. In ACM SIGGRAPH 2006 Papers, ACM, New York, SIGGRAPH ’06, 812–819. Google ScholarDigital Library
    23. Losasso, F., Talton, J., Kwatra, N., and Fedkiw, R. 2008. Two-way coupled sph and particle level set fluid simulation. IEEE Transactions on Visualization and Computer Graphics 14, 4 (July), 797–804. Google ScholarDigital Library
    24. Mihalef, V., Metaxas, D. N., and Sussman, M. 2009. Simulation of two-phase flow with sub-scale droplet and bubble effects. Comput. Graph. Forum 28, 2, 229–238.Google ScholarCross Ref
    25. Miyazaki, R., Dobashi, Y., and Nishita, T. 2002. Simulation of cumuliform clouds based on computational fluid dynamics. In EUROGRAPHICS 2002 Short Presentations, 405–410.Google Scholar
    26. Mizuno, R., Dobashi, Y., Chen, B.-Y., and Nishita, T. 2003. Physics motivated modeling of volcanic clouds as a two fluids model. In Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, IEEE Computer Society, Washington, DC, USA, PG ’03, 440–444. Google ScholarDigital Library
    27. Nielsen, M. B., and Christensen, B. B. 2010. Improved variational guiding of smoke animations. Comput. Graph. Forum 29, 2, 705–712.Google ScholarCross Ref
    28. Nielsen, M. B., Christensen, B. B., Zafar, N. B., Roble, D., and Museth, K. 2009. Guiding of smoke animations through variational coupling of simulations at different resolutions. In Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, ACM, New York, NY, USA, SCA ’09, 217–226. Google ScholarDigital Library
    29. Nielsen, M. B., 2013. https://code.google.com/p/two-continua-eulerian-spray-simulation/.Google Scholar
    30. O’Brien, J. F., and Hodgins, J. K. 1995. Dynamic simulation of splashing fluids. In Proceedings of Computer Animation, IEEE Computer Society, Washington, DC, USA, CA ’95, 198–205. Google ScholarDigital Library
    31. Peachey, D. R. 1986. Modeling waves and surf. In Proceedings of the 13th annual conference on Computer graphics and interactive techniques, ACM, New York, SIGGRAPH ’86, 65–74. Google ScholarDigital Library
    32. Pfaff, T., Thuerey, N., Selle, A., and Gross, M. 2009. Synthetic turbulence using artificial boundary layers. In ACM SIGGRAPH Asia 2009 papers, ACM, New York, SIGGRAPH Asia ’09, 121:1–121:10. Google ScholarDigital Library
    33. Selle, A., Rasmussen, N., and Fedkiw, R. 2005. A vortex particle method for smoke, water and explosions. In ACM SIGGRAPH 2005 Papers, ACM, New York, NY, USA, SIGGRAPH ’05, 910–914. Google ScholarDigital Library
    34. Shu, C.-W. 2009. High order weighted essentially non-oscillatory schemes for convection dominated problems. SIAM Review 51, 1, 82–126. Google ScholarDigital Library
    35. Sirignano, W. 1999. Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press.Google Scholar
    36. Song, O.-Y., Shin, H., and Ko, H.-S. 2005. Stable but nondissipative water. ACM Trans. Graph. 24, 1 (Jan.), 81–97. Google ScholarDigital Library
    37. Stam, J. 1999. Stable fluids. In Proceedings of the 26th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, SIGGRAPH ’99, 121–128. Google ScholarDigital Library
    38. Takahashi, T., Fujii, H., Kunimatsu, A., Hiwada, K., Saito, T., Tanaka, K., and Ueki, H. 2003. Realistic animation of fluid with splash and foam. Comput. Graph. Forum 22, 3, 391–400.Google ScholarCross Ref
    39. Thürey, N., Rüde, U., and Stamminger, M. 2006. Animation of open water phenomena with coupled shallow water and free surface simulations. In Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, Aire-la-Ville, Switzerland, SCA ’06, 157–164. Google ScholarDigital Library
    40. Tsai, R. Y.-h., Cheng, L.-t., Osher, S., and Zhao, H.-k. 2003. Fast sweeping algorithms for a class of hamilton-jacobi equations. SIAM Journal on Numerical Analysis 41, 673–694.Google ScholarCross Ref
    41. Villermaux, E., and Boss, B. 2009. Single-drop fragmentation determines size distribution of raindrops. Nature Physics.Google Scholar
    42. Zhang, X., and Shu, C.-W. 2011. Maximum-principle-satisfying and positivity-preserving high order schemes for conservation laws: Survey and new developments. Proceedings of the Royal Society A 467, 2752–2776.Google ScholarCross Ref


ACM Digital Library Publication:



Overview Page: