Animation of open water phenomena with coupled shallow water and free surface simulations

ABSTRACT

The goal of this paper is to perform simulations that capture fluid effects from small drops up to the propagation of large waves. To achieve this, we present a hybrid simulation method, that couples a two-dimensional shallow water simulation with a full three-dimensional free surface fluid simulation. We explain the approximations imposed by the shallow water model, and how to parametrize it according to the parameters of a 3D simulation. Each simulation is used to initialize double layered boundary conditions for the other one. The area covered by the 2D region can be an order of magnitude larger than the 3D region without significantly effecting the overall computation time. The 3D region can furthermore be easily moved within the 2D region during the course of the simulation. To achieve realistic results we combine our simulation method with a physically based model to generate and animate drops. For their generation we make use of the fluid turbulence model, and animate them with a simplified drag calculation. This allows simulations with relatively low resolutions.

REFERENCES

• 1: {BGD05} Buwa V., Gerlach D., Durst F.: Regimes of bubble formation on submerged orifices. Phys. Rev. Letters (April 2005). 2
• 2: {Del01} Dellar P. J.: Non-hydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations. Phys. Rev. E 65 (2001). 2
• 3: {DKvS99} Delnoij E., Kuipers J. A. M., van Swaaij W. P. M.: A three-dimensional CFG model for gas-liquid bubble columns. Chemical Engineering Science 54(1999). 2
• 4: Ronald P. Fedkiw , Tariq Aslam , Barry Merriman , Stanley Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), Journal of Computational Physics, v.152 n.2, p.457-492, July 1, 1999 [doi>10.1006/jcph.1999.6236]
• 5: {FdH*87} Frisch U., d'Humières D., Hasslacher B., Lallemand P., Pomeau Y., Rivert J.-P.: Lattice Gas Hydrodynamics in Two and Three Dimensions. Complex Systems 1 (1987), 649--707. 2
• 6: Nick Foster , Dimitri Metaxas, Realistic animation of liquids, Graphical Models and Image Processing, v.58 n.5, p.471-483, Sept. 1996 [doi>10.1006/gmip.1996.0039]
• 7: {HHL*05} Hagen T. R., Hjelmervik J. M., Lie K.-A., Natvig J. R., Henriksen M. O.: Visual simulation of shallow-water waves. Simulation Modelling Practice and Theory 13 (2005). 2
• 8: {HL97} He x., Luo L.-S.: A Priori Derivation of Lattice Boltzmann Equation. Phys. Rev. E 55 (1997), R6333-R6336. 2
• 9: {HNC02} Hinsinger D., Neyret F., Cani M.-P.: Interactive Animation of Ocean Waves. 2
• 10: {HSCD96} Hou S., Sterling J. D., Chen S., Doolen G.: A Lattice Boltzmann Subgrid Model for High Reynolds Number Flow. Fields Institute Communications 6 (1996), 151--166. 3
• 11: Geoffrey Irving , Eran Guendelman , Frank Losasso , Ronald Fedkiw, Efficient simulation of large bodies of water by coupling two and three dimensional techniques, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 12: {KAG*05} Keiser R., Adams B., Gasser D., Bazzi P., Dutre P., Gross M.: A Unified Lagrangian Approach to Solid-Fluid Animation. Proceedings of the 2005 Eurographics Symposium on Point-Based Graphics (2005). 2
• 13: Michael Kass , Gavin Miller, Rapid, stable fluid dynamics for computer graphics, ACM SIGGRAPH Computer Graphics, v.24 n.4, p.49-57, Aug. 1990
• 14: {KPR*05} Körner C., Pohl T., Rude U., Thürey N., Zeiser T.: Parallel Lattice Boltzmann Methods for CFD Applications. In Numerical Solution of Partial Differential Equations on Parallel Computers, Bruaset A., Tveito A., (Eds.), vol. 51 of LNCSE. Springer, 2005, pp. 439--465. 3
• 15: Frank Losasso , Frédéric Gibou , Ron Fedkiw, Simulating water and smoke with an octree data structure, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 16: Viorel Mihalef , Dimitris Metaxas , Mark Sussman, Animation and control of breaking waves, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028565]
• 17: {PK97} Pruppacher H. R., Klett J. D.: Microphysics of Clouds and Precipitation. Springer, 1997. 6
• 18: Nick Rasmussen , Duc Quang Nguyen , Willi Geiger , Ronald Fedkiw, Smoke simulation for large scale phenomena, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 19: {Sma63} Smagorinsky J.: General circulation experiments with the primitive equations. Mon. Wed. Rev. 91 (1963), 99--164. 3
• 20: Jos Stam, Stable fluids, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.121-128, July 1999 [doi>10.1145/311535.311548]
• 21: {Tes04} Tessendorf J.: Simulating Ocean Surfaces. SIGGRAPH 2004 Course Notes 31 (2004). 2, 8
• 22: {TFK*03} Takahashi T., Fujii H., Kunimatsu A., Hiwada K., Saito T., Tanaka K., Ueki H.: Realistic Animation of Fluid with Splash and Foam. Computer Graphics Forum 22 (3) (2003). 2, 7
• 23: {TPR*06} Thürey N., Pohl T., Rüde U., Oechsner M., Körner C.: Optimization and Stabilization of LBM Free Surface Flow Simulations using Adaptive Parameterization. Computers and Fluids 35 {8--9} (September-November 2006), 934--939. 4
• 24: {TR04} Thürey N., Rüde U.: Free Surface Lattice-Boltzmann fluid simulations with and without level sets. 199--208. Workshop on Vision, Modelling, and Visualization VMV. 2
• 25: Xiaoming Wei , Ye Zhao , Zhe Fan , Wei Li , Suzanne Yoakum-Stover , Arie Kaufman, Blowing in the wind, Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 26-27, 2003, San Diego, California
• 26: {Zho04} Zhou J. G.: Lattice Boltzmann Methods for Shallow Water Flows. Springer, 2004. 4

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.3 Applications