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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 51))

Summary

The lattice Boltzmann method (LBM) has evolved to a promising alternative to the well-established methods based on finite elements/volumes for computational fluid dynamics simulations. Ease of implementation, extensibility, and computational efficiency are the major reasons for LBM’s growing field of application and increasing popularity. In this paper we give a brief introduction to the involved theory and equations for LBM, present various techniques to increase the single-CPU performance, outline the parallelization of a standard LBM implementation, and show performance results. In order to demonstrate the straightforward extensibility of LBM, we then focus on an application in material science involving fluid flows with free surfaces. We discuss the required extensions to handle this complex scenario, and the impact on the parallelization technique.

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References

  1. S. Ansumali, I. V. Karlin, and S. Succi. Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky Model. Physica A, 338(3):379–394, 2004.

    Article  MathSciNet  Google Scholar 

  2. R. Argentini, A. Bakker, and C. Lowe. Efficiently Using Memory in Lattice Boltzmann Simulations. Future Generation Computer Systems, 20(6):973–980, 2004.

    Article  Google Scholar 

  3. J. Bernsdorf, F. Durst, and M. Schäfer. Comparison of Cellular Automata and Finite Volume Techniques for Simulation of Incompressible Flows in Complex Geometries. Int. J. Numer. Meth. Fluids, 29(3):251–264, 1999.

    Article  Google Scholar 

  4. V. Bhandari. Detailed Investigations of Transport Properties in Complex Reactor Components. Master thesis, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Erlangen, Germany, 2002.

    Google Scholar 

  5. P. Bhatnagar, E. P. Gross, and M. K. Krook. A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems. Phys. Rev., 94(3):511–525, 1954.

    Article  Google Scholar 

  6. M. Bouzidi, M. Firdaouss, and P. Lallemand. Momentum Transfer of a Boltzmann Lattice Fluid with Boundaries. Phys. Fluids, 13(11):3452–3459, 2001.

    Article  Google Scholar 

  7. S. Chapman and T. G. Cowling. The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, 1995.

    Google Scholar 

  8. H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot. Extended Boltzmann Kinetic Equation for Turbulent Flows. Science, 301(5644):633–636, 2003.

    Article  Google Scholar 

  9. S. Chen and G. D. Doolen. Lattice Boltzmann Method for Fluid Flows. Annu. Rev. Fluid Mech., 30:329–364, 1998.

    Article  MathSciNet  Google Scholar 

  10. S. Chen, G. D. Doolen, and K. G. Eggert. Lattice-Boltzmann Fluid Dynamics: A Versatile Tool for Multiphase and Other Complicated Flows. Los Alamos Science, 22:98–111, 1994.

    Google Scholar 

  11. S. Chen and D. Martinez. On Boundary Conditions in Lattice Boltzmann Methods. Phys. Fluids, 8(9):2527–2536, 1996.

    Article  MathSciNet  Google Scholar 

  12. B. Chopard and M. Droz. Cellular Automata Modeling of Physical Systems. Cambridge University Press, 1998.

    Google Scholar 

  13. C. Denniston, E. Orlandini, and J. Yeomans. Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics. Phys. Rev. E, 63:056702_10, 2001.

    Article  Google Scholar 

  14. S. Donath. On Optimized Implementations of the Lattice Boltzmann Method on Contemporary High Performance Architectures. Bachelor thesis, Lehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, 2004.

    Google Scholar 

  15. A. Dupuis and B. Chopard. Theory and Applications of an Alternative Lattice Boltzmann Grid Refinement Algorithm. Phys. Rev. E, 67(6):066707_7, 2003.

    Article  Google Scholar 

  16. O. Filippova and D. Hänel. Grid Refinement for Lattice BGK Models. J. Comput. Phys., 147:219–228, 1998.

    Article  Google Scholar 

  17. U. Frisch, D. d’Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet. Lattice Gas Hydrodynamics in Two and Three Dimensions. Complex Systems, 1:649–707, 1987.

    MathSciNet  Google Scholar 

  18. S. Geller, M. Krafczyk, J. Tölke, S. Turek, and J. Hron. Benchmark Computations based on Lattice Boltzmann, Finite Element, and Finite Volume Methods for Laminar Flows. Submitted to Computers and Fluids, 2004. Also available as Ergebisbericht 274 des Fachbereichs Mathematik der Universtität Dortmund, http://www.mathematik.uni-dortmund.de/lsiii/german/preprintfb.html.

    Google Scholar 

  19. I. Ginzburg and P. M. Adler. Boundary Flow Condition Analysis for Three-Dimensional Lattice Boltzmann Model. J. Phys. II France, 4:191–214, 1994.

    Article  Google Scholar 

  20. I. Ginzburg and D. d’Humières. Multireflection Boundary Conditions for Lattice Boltzmann Models. Phys. Rev. E, 68(6):066614_30, 2003.

    Article  Google Scholar 

  21. A. S. Glassner. An Introduction to Ray Tracing. Harlekijn, 1989.

    Google Scholar 

  22. X. He and G. D. Doolen. Thermodynamic Foundations of Kinetic Theory and Lattice Boltzmann Models for Multiphase Flows. J. Stat. Phys., 107(1–2):309–328, 2002.

    Article  Google Scholar 

  23. X. He and L.-S. Luo. A Priori Derivation of the Lattice Boltzmann Equation. Phys. Rev. E, 55(6):R6333–R6336, 1997.

    Article  Google Scholar 

  24. F. Hülsemann, M. Kowarschik, M. Mohr, and U. Rüde. Parallel geometric multigrid. In A. M. Bruaset and A. Tveito, editors, Numerical Solution of Partial Differential Equations on Parallel Computers, volume 51 of Lecture Notes in Computational Science and Engineering, pages 165–208. Springer-Verlag, 2005.

    Google Scholar 

  25. K. Iglberger. Cache Optimizations for the Lattice Boltzmann Method in 3D. Studienarbeit, Lehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, 2003.

    Google Scholar 

  26. D. Kehrwald. Numerical Analysis of Immiscible Lattice BGK. PhD thesis, Fachbereich Mathematik, Universität Kaiserslautern, 2002.

    Google Scholar 

  27. M. Kowarschik. Data Locality Optimizations for Iterative Numerical Algorithms and Cellular Automata on Hierarchical Memory Architectures. PhD thesis, Universität Erlangen-Nürnberg, Technische Fakultät, 2004.

    Google Scholar 

  28. A. J. C. Ladd. Numerical Simulations of Particulate Suspensions via a Discrete Boltzmann Equation. Part 1. Theoretical Foundation. J. Fluid Mech., 271:285–309, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  29. G. Marmitt, A. Kleer, I. Wald, H. Friedrich, and P. Slusallek. Fast and Accurate Ray-Voxel Intersection Techniques for Iso-Surface Ray Tracing. In Vision, Modelling, and Visualization 2003 (VMV), November 16–18, Stanford (CA), USA, 2004.

    Google Scholar 

  30. G. R. McNamara and G. Zanetti. Use of the Boltzmann Equation to Simulate Lattice Gas Automata. Phys. Rev. Lett., 61:2332–2335, 1988.

    Article  Google Scholar 

  31. W. Miller and S. Succi. A Lattice Boltzmann Model for Anisotropic Crystal Growth from Melt. J. Stat. Phys., 107(1–2):173–186, 2002.

    Article  Google Scholar 

  32. C. Pan, J. Prins, and C. T. Miller. A High-Performance Lattice Boltzmann Implementation to Model Flow in Porous Media. Comp. Phys. Com., 158(1):89–105, 2004.

    Article  Google Scholar 

  33. T. Pohl, F. Deserno, N. Thürey, U. Rüde, P. Lammers, G. Wellein, and T. Zeiser. Performance Evaluation of Parallel Large-Scale Lattice Boltzmann Applications on Three Supercomputing Architectures. In Supercomputing Conference, 2004.

    Google Scholar 

  34. T. Pohl, M. Kowarschik, J. Wilke, K. Iglberger, and U. Rüde. Optimization and Profiling of the Cache Performance of Parallel Lattice Boltzmann Codes. Parallel Processing Letters, 13(4):549–560, 2003.

    Article  MathSciNet  Google Scholar 

  35. Y. H. Qian, D. d’Humières, and P. Lallemand. Lattice BGK Models for Navier-Stokes Equation. Europhys. Lett., 17(6):479–484, 1992.

    Google Scholar 

  36. D. H. Rothman and S. Zaleski. Lattice Gas Cellular Automata. Simple models of Complex Hydrodynamics. Cambridge University Press, 1997.

    Google Scholar 

  37. M. Schulz, M. Krafczyk, J. Tölke, and E. Rank. Parallelization Strategies and Efficiency of CFD Computations in Complex Geometries Using Lattice Boltzmann Methods on High Performance Computers. In M. Breuer, F. Durst, and C. Zenger, editors, High Performance Scientific and Engineering Computing, pages 115–122, Berlin, 2001. Springer.

    Google Scholar 

  38. P. Shirley and K. Sung. Graphics Gems III. Morgan Kaufmann, 1994.

    Google Scholar 

  39. S. Succi. The Lattice Boltzmann Equation — For Fluid Dynamics and Beyond. Clarendon Press, 2001.

    Google Scholar 

  40. I. Wald, C. Benthin, M. Wagner, and P. Slusallek. Interactive Rendering with Coherent Ray Tracing. In A. Chalmers and T.-M. Rhyne, editors, Computer Graphics Forum (Proceedings of EUROGRAPHICS 2001), volume 20. Blackwell Publishers, Oxford, 2001.

    Google Scholar 

  41. G. Wellein, T. Zeiser, S. Donath, and G. Hager. On the Single Processor Performance of Simple Lattice Boltzmann Kernels. Computers & Fluids, accepted, 2004.

    Google Scholar 

  42. J. Wilke. Cache Optimizations for the Lattice Boltzmann Method in 2D. Studienarbeit, Lehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, 2002.

    Google Scholar 

  43. J. Wilke, T. Pohl, M. Kowarschik, and U. Rüde. Cache Performance Optimization for Parallel Lattice Boltzmann Code in 2D. Technical Report 03-3, Lehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, 2003.

    Google Scholar 

  44. D. A. Wolf-Gladrow. Lattice Gas Cellular Automata and Lattice Boltzmann Models, volume 1725 of Lecture Notes in Mathematics. Springer, Berlin, 2000.

    Google Scholar 

  45. S. Wolfram. Cellular Automaton Fluids 1: Basic Theory. J. Stat. Phys., 3/4:471–526, 1986.

    Article  MathSciNet  Google Scholar 

  46. D. Yu, R. Mei, L.-S. Luo, and W. Shyy. Viscous Flow Computations with the Method of Lattice Boltzmann Equation. Progr. Aero. Sci., 39:329–367, 2003.

    Article  Google Scholar 

  47. D. Yu, R. Mei, and W. Shyy. A Multiblock Lattice Boltzmann Method for Viscous Fluid Flows. Int. J. Numer. Meth. Fluids, 39(2):99–120, 2002.

    Article  Google Scholar 

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Körner, C., Pohl, T., Rüde, U., Thürey, N., Zeiser, T. (2006). Parallel Lattice Boltzmann Methods for CFD Applications. In: Bruaset, A.M., Tveito, A. (eds) Numerical Solution of Partial Differential Equations on Parallel Computers. Lecture Notes in Computational Science and Engineering, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31619-1_13

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