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Issue No.05 - September/October (2009 vol.15)
pp: 802-814
Kaloian Petkov , Stony Brook University, Stony Brook
Feng Qiu , Stony Brook University, Stony Brook
Zhe Fan , Stony Brook University, Stony Brook
Arie E. Kaufman , Stony Brook University, Stony Brook
Klaus Mueller , Stony Brook University, Stony Brook
The Lattice Boltzmann method (LBM) for visual simulation of fluid flow generally employs cubic Cartesian (CC) lattices such as the D3Q13 and D3Q19 lattices for the particle transport. However, the CC lattices lead to suboptimal representation of the simulation space. We introduce the face-centered cubic (FCC) lattice, fD3Q13, for LBM simulations. Compared to the CC lattices, the fD3Q13 lattice creates a more isotropic sampling of the simulation domain and its single lattice speed (i.e., link length) simplifies the computations and data storage. Furthermore, the fD3Q13 lattice can be decomposed into two independent interleaved lattices, one of which can be discarded, which doubles the simulation speed. The resulting LBM simulation can be efficiently mapped to the GPU, further increasing the computational performance. We show the numerical advantages of the FCC lattice on channeled flow in 2D and the flow-past-a-sphere benchmark in 3D. In both cases, the comparison is against the corresponding CC lattices using the analytical solutions for the systems as well as velocity field visualizations. We also demonstrate the performance advantages of the fD3Q13 lattice for interactive simulation and rendering of hot smoke in an urban environment using thermal LBM.
Lattice Boltzmann method, face-centered cubic, fD3Q13, D3Q13, D3Q19, GPU.
Kaloian Petkov, Feng Qiu, Zhe Fan, Arie E. Kaufman, Klaus Mueller, "Efficient LBM Visual Simulation on Face-Centered Cubic Lattices", IEEE Transactions on Visualization & Computer Graphics, vol.15, no. 5, pp. 802-814, September/October 2009, doi:10.1109/TVCG.2009.32
[1] 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/Aug. 2009.
[2] U. Behrens and R. Ratering, “Adding Shadows to a Texture-Based Volume Renderer,” Proc. IEEE Symp. Volume Visualization, pp.39-46, 1998.
[3] M. Bouzidi, M. Firdaouss, and P. Lallemand, “Momentum Transfer of a Boltzmann-Lattice Fluid with Boundaries,” Physics of Fluids, vol. 13, no. 11, pp.3452-3459, 2001.
[4] B. Cabral and L.C. Leedom, “Imaging Vector Fields Using Line Integral Convolution,” Proc. ACM SIGGRAPH '93, pp.263-270, 1993.
[5] S. Chen and G.D. Doolen, “Lattice Boltzmann Method for Fluid Flows,” Ann. Rev. Fluid Mechanics, vol. 30, pp.329-364, 1998.
[6] J.H. Conway, N.J.A. Sloane, and E. Bannai, Sphere-Packings, Lattices, and Groups. Springer-Verlag, 1987.
[7] D. D'Humières, M. Bouzidi, and P. Lallemand, “Thirteen-Velocity Three-Dimensional Lattice Boltzmann Model,” Physical Rev. E, vol. 63, p.066702, 2001.
[8] D. D'Humières, I. Ginzburg, M. Krafczyk, P. Lallemand, and L.-S. Luo, “Multiple-Relaxation-Time Lattice Boltzmann Models in Three Dimensions,” Royal Soc. London Philosophical Trans. Series A 360, vol. 1792, pp.437-451, 2002.
[9] A. Entezari, “Optimal Sampling Lattices and Trivariate Box Splines,” PhD thesis, Simon Fraser Univ., 2007.
[10] R. Fedkiw, J. Stam, and H.W. Jensen, “Visual Simulation of Smoke,” Proc. ACM SIGGRAPH '01, pp.15-22, 2001.
[11] Z.-G. Feng and E.E. Michaelides, “Hydrodynamic Force on Spheres in Cylindrical and Prismatic Enclosures,” Int'l J. Multiphase Flow, vol. 28, no. 3, pp.479-496, 2002.
[12] U. Frisch, B. Hasslacher, and Y. Pomeau, “Lattice-Gas Automata for the Navier-Stokes Equation,” Physical Rev. Letters, vol. 56, no. 14, pp.1505-1508, 1986.
[13] S. Hou, J. Sterling, S. Chen, and G.D. Doolen, “A Lattice Boltzmann Subgrid Model for High Reynolds Number Flows,” Computer, pp.1004-1022, 1994.
[14] T.A. Johnson and V.C. Patel, “Flow Past a Sphere up to a Reynolds Number of 300,” J. Fluid Mechanics, vol. 378, pp.19-70, 1999.
[15] D. Kim, H. Choi, and H. Choi, “Characteristics of Laminar Flow Past a Sphere in Uniform Shear,” Physics of Fluids, vol. 17, no. 10, p.103602, 2005.
[16] J. Krüger and R. Westermann, “Acceleration Techniques for GPU-Based Volume Rendering,” Proc. IEEE Visualization Conf., pp.38-45, 2003.
[17] P. Lallemand and L.-S. Luo, “Theory of the Lattice Boltzmann Method: Acoustic and Thermal Properties in Two and Three Dimensions,” Physical Rev. E, vol. 68, no. 3, pp.036706-+, 2003.
[18] J. Latt, “Choice of Units in Lattice Boltzmann Simulations,” technical report,, 2008.
[19] R.S. Maier, R.S. Bernard, and D.W. Grunau, “Boundary Conditions for the Lattice Boltzmann Method,” Physics of Fluids, vol. 8, no. 7, pp.1788-1801, 1996.
[20] R. Mei, W. Shyy, D. Yu, and L.-S. Luo, “Lattice Boltzmann Method for 3-d Flows with Curved Boundary,” J. Computational Physics, vol. 161, no. 2, pp.680-699, 2000. 350006.
[21] NVIDIA, Compute Unified Device Architecture Programming Guide, 2008. Version 2.0, html , 2009.
[22] F. Qiu, F. Xu, Z. Fan, N. Neophytos, A. Kaufman, and K. Mueller, “Lattice-Based Volumetric Global Illumination,” IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 6, pp.1576-1583, Nov./Dec. 2007.
[23] J. Stam, “Stable Fluids,” Proc. ACM SIGGRAPH '99, pp.121-128, 1999.
[24] N. Thuerey and U. Ruede, “Free Surface Lattice-Boltzmann Fluid Simulations with and without Level Sets,” Proc. Vision, Modeling, and Visualization Conf., pp.199-207, 2004.
[25] R. Verberg and A.J. C. Ladd, “Lattice-Boltzmann Model with Sub-Grid-Scale Boundary Conditions,” Physical Rev. Letters, vol. 84, no. 10, pp.2148-2151, 2000.
[26] X. Wei, Y. Zhao, Z. Fan, W. Li, F. Qiu, S. Yoakum-Stover, and A. Kaufman, “Lattice-Based Flow Field Modeling,” IEEE Trans. Visualization and Computer Graphics, vol. 10, no. 6, pp.719-729, Nov./Dec. 2004.
[27] S.-B. Wen and C.-L. Lai, “Theoretical Analysis of Flow Passing a Single Sphere Moving in a Micro-Tube,” Proc. Royal Soc. Math. Physical and Eng. Sciences, vol. 459, no. 2030, pp.495-526, 2003.
[28] R.M. Wham, O.A. Basaran, and C.H. Byers, “Wall Effects on Flow Past Solid Spheres at Finite Reynolds Number,” Industrial & Eng. Chemistry Research, vol. 35, no. 3, pp.864-874, 1996.
[29] D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction, first ed. Springer-Verlag, 2000.
[30] Y. Zhao, Y. Han, Z. Fan, F. Qiu, Y.-C. Kuo, A. 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./Feb. 2007.
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