Stable and efficient miscible liquid-liquid interactions

ABSTRACT

In our surrounding environment, we may often see many various miscible liquid-liquid mixture phenomena, like pouring honey or ink into water, Coca Cola into strong wine etc., while few papers have devoted to the simulation of the phenomena. In this paper, we use a two-fluid lattice Boltzmann method (TFLBM) to simulate the underlying dynamics of miscible mixtures. By the method, a subgrid model is applied to improve its numerical stability so that the free surface of the mixture, accompanying with higher Reynolds number, can be simulated. We also apply control forces to the mixture with interesting animation created. By optimizing the memory structure and taking the advantage of dual-core or multi-core systems, we achieve real time computation for a domain in 64³ cells full of fluid mixtures.

REFERENCES

• 1: Bhatnagar, P. L., Gross, E. P., and Krook, M. 1954. A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Physical Review 94, 3, 511--525.
• 2: D'Humieres, D., Ginzburg, I., Krafczyk, M., Lallemand, P., and Luo, L. 2002. Multiple-relaxation-time lattice boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437--451.
• 3: Donath, S., 2004. On optimized implementations of the lattice boltzmann method on contemporary high performance architectures.
• 4: Douglas Enright , Stephen Marschner , Ronald Fedkiw, Animation and rendering of complex water surfaces, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 5: Z. Fan , Y. Zhao , A. Kaufman , Y. He, Adapted unstructured LBM for flow simulation on curved surfaces, Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 29-31, 2005, Los Angeles, California [doi>10.1145/1073368.1073404]
• 6: Raanan Fattal , Dani Lischinski, Target-driven smoke animation, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 7: Ronald Fedkiw , Jos Stam , Henrik Wann Jensen, Visual simulation of smoke, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.15-22, August 2001 [doi>10.1145/383259.383260]
• 8: Nick Foster , Ronald Fedkiw, Practical animation of liquids, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.23-30, August 2001 [doi>10.1145/383259.383261]
• 9: 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]
• 10: Nick Foster , Dimitris Metaxas, Controlling Fluid Animation, Proceedings of the 1997 Conference on Computer Graphics International, p.178, June 23-27, 1997
• 11: Ginzburg, I., and Steiner, K. 2002. Free surface lattice boltzmann method to model the filling of expanding cavities by bingham fluids. Phil. Trans. R. Soc. Lond. A. 360, 453--466.
• 12: S. T. Greenwood , D. H. House, Better with bubbles: enhancing the visual realism of simulated fluid, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028562]
• 13: Jeong-Mo Hong , Chang-Hun Kim, Controlling fluid animation with geometric potential: Research Articles, Computer Animation and Virtual Worlds, v.15 n.3-4, p.147-157, July 2004 [doi>10.1002/cav.v15:3/4]
• 14: Hou, S., Sterling, J., Chen, S., and Doolen, G. D. 1996. A lattice subgrid model for high reynolds number flows. Fields Inst. Comm. 6, 151--166.
• 15: Insung Ihm , Byungkwon Kang , Deukhyun Cha, Animation of reactive gaseous fluids through chemical kinetics, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028550]
• 16: Arnauld Lamorlette , Nick Foster, Structural modeling of flames for a production environment, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 17: William E. Lorensen , Harvey E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.163-169, July 1987
• 18: Losasso, L., Shinar, D., Selle, A., and Fedkiw, R. 2006. Better with bubbles: Enhancing the visual realism of simulated fluid. ACM Transactions on Graphics (TOG) 25, 3, 812--819.
• 19: Luo, L. S., and Girimaji, S. S. 2003. Theory of the lattice boltzmann method: two-fluid model for binary mixtures. Physical Review E 67, 3, 036302.
• 20: Hai Mao , Yee-Hong Yang, Particle-based immiscible fluid-fluid collision, Proceedings of Graphics Interface 2006, June 07-09, 2006, Quebec, Canada
• 21: Antoine McNamara , Adrien Treuille , Zoran Popović , Jos Stam, Fluid control using the adjoint method, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 22: Matthias Müller , Barbara Solenthaler , Richard Keiser , Markus Gross, Particle-based fluid-fluid interaction, Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 29-31, 2005, Los Angeles, California [doi>10.1145/1073368.1073402]
• 23: Mebarki, A., Alliez, P., and Devillers, O. 2005. Farthest point seeding for efficient placement of streamlines. Proc. of IEEE Visualization, 479--486.
• 24: Ryoichi Mizuno , Yoshinori Dobashi , Bing-Yu Chen , Tomoyuki Nishita, Physics Motivated Modeling of Volcanic Clouds as a Two Fluids Model, Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, p.440, October 08-10, 2003
• 25: Duc Quang Nguyen , Ronald Fedkiw , Henrik Wann Jensen, Physically based modeling and animation of fire, Proceedings of the 29th annual conference on Computer graphics and interactive techniques, July 23-26, 2002, San Antonio, Texas
• 26: POV-RAY. www.povray.org.
• 27: Povitsky, A. 2001. High-incidence 3d lid-driven cavity flow. American Institute of Aeronautics and Astronautics. AIAA Paper 01-2847, 1--7.
• 28: Premože, S., Tasdizen, T., Bigler, J., Lefohn, A., and Whitaker, R. T. 2003. Particle-based simulation of fluids. Eurographics2003 22, 3, 401--410.
• 29: N. Rasmussen , D. Enright , D. Nguyen , S. Marino , N. Sumner , W. Geiger , S. Hoon , R. Fedkiw, Directable photorealistic liquids, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028549]
• 30: Lin Shi , Yizhou Yu, Controllable smoke animation with guiding objects, ACM Transactions on Graphics (TOG), v.24 n.1, p.140-164, January 2005 [doi>10.1145/1037957.1037965]
• 31: Lin Shi , Yizhou Yu, Taming liquids for rapidly changing targets, Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 29-31, 2005, Los Angeles, California [doi>10.1145/1073368.1073401]
• 32: Smagorinski, J. 1963. General circulation experiments with the primitive equations i: the basic experiments. Monthly Weather Rev. 91, 99.
• 33: 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]
• 34: Succi, S. 2001. The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press, U.K.
• 35: Sumner, N., Hoon, S., Geiger, W., Marino, S., Rasmussen, N., and Fedkiw, R. 2003. Melting and terminatrix. In SIGGRAPH 2003 Sketches & Applications.
• 36: Thürey, N., and Rüde, U. 2004. Free surface lattice-boltzmann fluid simulations with and without level sets. Workshop on Vision, Modeling and Visualization, 199--208.
• 37: N. Thürey , R. Keiser , M. Pauly , U. Rüde, Detail-preserving fluid control, Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, September 02-04, 2006, Vienna, Austria
• 38: Adrien Treuille , Antoine McNamara , Zoran Popović , Jos Stam, Keyframe control of smoke simulations, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 39: Enhua Wu , Youquan Liu , Xuehui Liu, An improved study of real-time fluid simulation on GPU: Research Articles, Computer Animation and Virtual Worlds, v.15 n.3-4, p.139-146, July 2004 [doi>10.1002/cav.v15:3/4]
• 40: Yu, H., Luo, L., and Girimaji, S. 2006. Les of turbulent square jet flow using an mrt lattice boltzmann model. Computers & Fluids 35, 957--965.
• 41: Zhao, Y., Wang, L., Qiu, F., Kaufman, A., and Mueller, K. 2006. Melting and flowing in multiphase environment. Computers & Graphics 30, 4, 519--528.
• 42: Hongbin Zhu , Xuehui Liu , Youquan Liu , Enhua Wu, Simulation of miscible binary mixtures based on lattice Boltzmann method: Research Articles, Computer Animation and Virtual Worlds, v.17 n.3-4, p.403-410, July 2006 [doi>10.1002/cav.v17:3/4]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Physically based modeling

Keywords:
control, free surface, lattice Boltzmann method, memory optimization, miscible mixture, multicore system, stability, subgrid model