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Issue No.02 - Feb. (2014 vol.20)
pp: 289-302
Xiaopei Liu , Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
Wai-Man Pang , Caritas Inst. of Higher Educ., Hong Kong, China
Jing Qin , Dept. of Comput. Sci. & Eng., Chinese Univ. of Hong Kong, Hong Kong, China
Chi-Wing Fu , Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore, Singapore
ABSTRACT
This paper presents a novel approach to simulating turbulent flows by developing an adaptive multirelaxation scheme in the framework of lattice Boltzmann equation (LBE). Existing LBE methods in graphics simulations are usually insufficient for turbulent flows since the collision term disturbs the underlying stability and accuracy. We adopt LBE with the multiple relaxation time (MRT) collision model (MRT-LBE), and address this issue by enhancing the collision-term modeling. First, we employ renormalization group analysis and formulate a new turbulence model with an adaptive correction method to compute more appropriate eddy viscosities on a uniform lattice structure. Efficient algebraic calculations are retained with small-scale turbulence details while maintaining the system stability. Second, we note that for MRT-LBE, predicting single eddy viscosity per lattice node may still result in instability. Hence, we simultaneously predict multiple eddy viscosities for stress-tensor-related elements, thereby asynchronously computing multiple relaxation parameters to further enhance the MRT-LBE stability. With these two new strategies, turbulent flows can be simulated with finer visual details even on coarse grid configurations. We demonstrate our results by simulating and visualizing various turbulent flows, particularly with smoke animations, where stable turbulent flows with high Reynolds numbers can be faithfully produced.
INDEX TERMS
Computational modeling, Mathematical model, Viscosity, Numerical models, Adaptation models, Lattice Boltzmann methods,multiple relaxation time model, Computational modeling, Mathematical model, Viscosity, Numerical models, Adaptation models, Lattice Boltzmann methods, turbulence modeling, Turbulence simulation, lattice Boltzmann models
CITATION
Xiaopei Liu, Wai-Man Pang, Jing Qin, Chi-Wing Fu, "Turbulence Simulation by Adaptive Multi-Relaxation Lattice Boltzmann Modeling", IEEE Transactions on Visualization & Computer Graphics, vol.20, no. 2, pp. 289-302, Feb. 2014, doi:10.1109/TVCG.2012.303
REFERENCES
[1] R. Fedkiw, J. Stam, and H.W. Jensen, “Visual Simulation of Smoke,” Proc. SIGGRAPH '01, pp. 15-22, 2001.
[2] A. Selle, N. Rasmussen, and R. Fedkiw, “A Vortex Particle Method for Smoke, Water and Explosions,” ACM Trans. Graphics, vol. 24, no. 3, pp. 910-914, 2005.
[3] T. Kim, N. Thürey, D. James, and M. Gross, “Wavelet Turbulence for Fluid Simulation,” ACM Trans. Graphics, vol. 27, no. 3, pp. 50:1-50:6, Aug. 2008.
[4] T. Pfaff, N. Thuerey, A. Selle, and M. Gross, “Synthetic Turbulence Using Artificial Boundary Layers,” ACM Trans. Graphics, vol. 28, no. 5, pp. 121:1-121:10, Dec. 2009.
[5] P. Mullen, K. Crane, D. Pavlov, Y. Tong, and M. Desbrun, “Energy-Preserving Integrators for Fluid Animation,” ACM Trans. Graphics, vol. 28, no. 3, pp. 38:1-38:8, July 2009.
[6] U.R. Alim, A. Entezari, and T. Möller, “The Lattice-Boltzmann Method on Optimal Sampling Lattices,” IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 4, pp. 630-641, July 2009.
[7] K. Petkov, F. Qiu, Z. Fan, A.E. Kaufman, and K. Mueller, “Efficient LBM Visual Simulation on Face-Centered Cubic Lattices,” IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 5, pp. 802-814, Sept. 2009.
[8] Y. Zhao, L. Wang, F. Qiu, A. Kaufman, and K. Mueller, “Melting and Flowing in Multiphase Environment,” Computers & Graphics, vol. 30, no. 4, pp. 519-528, 2006.
[9] M. Johan and S. Pierre, “On the Model Coefficients for the Standard and the Variational Multi-Scale Smagorinsky Model,” J. Fluid Mechanics, vol. 569, pp. 287-319, 2006.
[10] X. Wei, Y. Zhao, Z. Fan, W. Li, F. Qiu, S. Yoakum-Stover, and A.E. Kaufman, “Lattice-Based Flow Field Modeling,” IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 6, pp. 719-729, Nov. 2004.
[11] H. Yu, L.-S. Luo, and S.S. Girimaji, “LES of Turbulent Square Jet Flow Using an MRT Lattice Boltzmann Model,” Computers & Fluids, vol. 35, nos. 8-9, pp. 957-965, 2006.
[12] L. Pierre and L.-S. Luo, “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Physical Rev. E, vol. 61, no. 6, pp. 6546-6562, 2000.
[13] D. D'Humieres, G. Irina, K. Manfred, L. Pierre, and L.-S. Luo, “Multiple-Relaxation-Time Lattice Boltzmann Models in Three Dimensions,” Philosophical Trans. Royal Soc.of London Series A-Math. Physical and Eng. Sciences, vol. 360, no. 1792, pp. 437-451, 2002.
[14] S. Succi, O. Filippova, H. Chen, and S. Orszag, “Towards a Renormalized Lattice Boltzmann Equation for Fluid Turbulence,” J. Statistical Physics, vol. 107, pp. 261-278, 2002.
[15] K. Perlin, “An Image Synthesizer,” Proc. SIGGRAPH '85, pp. 287-296, 1985.
[16] G.Y. Gardner, “Visual Simulation of Clouds,” Proc. SIGGRAPH '85, pp. 297-304, 1985.
[17] D.S. Ebert and R.E. Parent, “Rendering and Animation of Gaseous Phenomena by Combining Fast Volume and Scanline A-Buffer Techniques,” Proc. SIGGRAPH '90, pp. 357-366, 1990.
[18] N. Foster and D. Metaxas, “Modeling the Motion of a Hot, Turbulent Gas,” Proc. SIGGRAPH '97, pp. 181-188, 1997.
[19] J. Stam, “Stable Fluids,” Proc. SIGGRAPH '99, pp. 121-128, 1999.
[20] A. Lamorlette and N. Foster, “Structural Modeling of Flames for a Production Environment,” ACM Trans. Graphics, vol. 21, no. 3, pp. 729-735, July 2002.
[21] N. Rasmussen, D.Q. Nguyen, W. Geiger, and R. Fedkiw, “Smoke Simulation for Large Scale Phenomena,” ACM Trans. Graphics, vol. 22, no. 3, pp. 703-707, July 2003.
[22] R. Bridson, J. Houriham, and M. Nordenstam, “Curl-Noise for Procedural Fluid Flow,” ACM Trans., vol. 26, no. 3, July 2007.
[23] R. Narain, J. Sewall, M. Carlson, and M.C. Lin, “Fast Animation of Turbulence Using Energy Transport and Procedural Synthesis,” ACM Trans. Graphics, vol. 27, no. 5, pp. 166:1-166:8, Dec. 2008.
[24] T. Pfaff, N. Thuerey, J. Cohen, S. Tariq, and M. Gross, “Scalable Fluid Simulation Using Anisotropic Turbulence Particles,” ACM Trans. Graphics, vol. 29, no. 6, pp. 174:1-174:8, Dec. 2010.
[25] Y. Zhao, Z. Yuan, and F. Chen, “Enhancing Fluid Animation with Adaptive, Controllable and Intermittent Turbulence,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 75-84, 2010.
[26] F. Chen, Y. Zhao, and Z. Yuan, “Langevin Particle: A Self-Adaptive Lagrangian Primitive for Flow Simulation Enhancement,” Computer Graphics Forum, vol. 30, no. 2, pp. 435-444, 2011.
[27] M. Lentine, W. Zheng, and R. Fedkiw, “A Novel Algorithm for Incompressible Flow Using Only a Coarse Grid Projection,” ACM Trans. Graphics, vol. 29, no. 4, pp. 114:1-114:9, July 2010.
[28] B. Kim, Y. Liu, I. Llamas, and J. Rossignac, “Advections with Significantly Reduced Dissipation and Diffusion,” IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 1, pp. 135-144, Jan. 2007.
[29] C. Min and F. Gibou, “A Second Order Accurate Projection Method for the Incompressible Navier-Stokes Equations on Non-Graded Adaptive Grids,” J. Computational Physics, vol. 219, no. 2, pp. 912-929, Dec. 2006.
[30] A. Selle, R. Fedkiw, B. Kim, Y. Liu, and J. Rossignac, “An Unconditionally Stable Maccormack Method,” J. Scientific Computing, vol. 35, nos. 2-3, pp. 350-371, June 2008.
[31] M. Müller, D. Charypar, and M. Gross, “Particle-Based Fluid Simulation for Interactive Applications,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 154-159, 2003.
[32] S. Premoze, T. Tasdizen, J. Bigler, A. Lefohn, and R.T. Whitaker, “Particle-Based Simulation of Fluids,” Computer Graphics Forum, vol. 22, no. 3, pp. 401-410, 2003.
[33] C. Hudong, C. Shiyi, and W.H. Matthaeus, “Recovery of the Navier-Stokes Equations Using a Lattice-Gas Boltzmann Method,” Physical Rev. A, vol. 45, no. 8, pp. R5339-R5342, 1992.
[34] W. Li, X. Wei, and A. Kaufman, “Implementing Lattice Boltzmann Computation on Graphics Hardware,” The Visual Computer, vol. 19, pp. 444-456, 2003.
[35] N. Thürey, T. Pohl, U. Rüde, M. Öchsner, and C. Körner, “Optimization and Stabilization of LBM Free Surface Flow Simulations Using Adaptive Parameterization,” Computers and Fluids, vol. 35, nos. 8/9, pp. 934-939, Sept.-Nov. 2006.
[36] K. Iglberger, N. Thürey, and U. Rüde, “Simulation of Moving Particles in 3D with the Lattice Boltzmann Method,” Computers & Math. with Applications, Mesoscopic Methods in Eng. and Science, vol. 55, no. 7, pp. 1363-1628, Apr. 2008.
[37] C. Körner, T. Pohl, U. Rüde, N. Thürey, and T. Zeiser, “Parallel Lattice Boltzmann Methods for CFD Applications,” Numerical Solution of Partial Differential Equations on Parallel Computers, vol. 51, pp. 439-465, 2006.
[38] X. Wei, W. Li, K. Mueller, and A. Kaufman, “Simulating Fire with Texture Splats,” Proc. IEEE Visualization '02, pp. 227-235, 2002.
[39] Y. Zhao, Y. Han, Z. Fan, F. Qiu, Y.-C. Kuo, A.E. Kaufman, and K. Mueller, “Visual Simulation of Heat Shimmering and Mirage,” IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 1, pp. 179-189, Jan. 2007.
[40] N.S.-H. Chu and C.-L. Tai, “MoXi: Real-Time Ink Dispersion in Absorbent Paper,” ACM Trans. Graphics, vol. 24, no. 3, pp. 504-511, July 2005.
[41] P.L. Bhatnagar, E.P. Gross, and M. Krook, “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,” Physical Rev., vol. 94, no. 3, pp. 511-525, http://link.aps.org/doi/10.1103PhysRev.94.511 , May 1954.
[42] J. Anderson, E. Dick, G. Degrez, R. Grundmann, J. Degroote, and J. Vierendeels, Computational Fluid Dynamics: An Introduction, third ed., J.F. Wendt, ed. Springer, 2009.
[43] O. Filippova, S. Succi, F. Mazzocco, C. Arrighetti, G. Bella, and D. Hänel, “Multiscale Lattice Boltzmann Schemes with Turbulence Modeling,” J. Computational Physics, vol. 170, no. 2, pp. 812-829, 2001.
[44] S.B. Pope, Turbulent Flows. Cambridge Univ. Press, 2000.
[45] L. Davidson and S.H. Peng, “Hybrid LES-RANS Modelling: A One-Equation SGS Model Combined with a k-$\omega$ Model for Predicting Recirculating Flows,” Int'l J. for Numerical Methods in Fluids, vol. 43, pp. 1003-1018, 2003.
[46] D. Yu, R. Mei, and S. Wei, “Improved Treatment of the Open Boundary in the Method of Lattice Boltzmann Equation,” Progress in Computational Fluid Dynamics, vol. 5, nos. 1-2, pp. 3-12, 2005.
[47] K. Engel, M. Hadwiger, J.M. Kniss, C. Rezk-Salama, and D. Weiskopf, Real-Time Volume Graphics. AK Peters, 2006.
[48] M. Lesieur, O. Métais, and P. Comte, Large-Eddy Simulations of Turbulence. Cambridge Univ. Press, 2005.
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