Combination of Detailed CFD Simulations Using the Lattice Boltzmann Method and Experimental Measurements Using the NMR/MRI Technique

  • Thomas Zeiser


In the last decades, tremendous progress has been made in the area of numerical methods and computer technology but also new experimental techniques evolved and have been transferred to new application areas. This article describes the combination of two recent and innovative techniques. On the numerical side, the lattice Boltzmann method (LBM) is used for detailed simulations of the flow in complicated 3-D structures. On the experimental side, the principles of nuclear magnetic resonance (NMR) are exploited to scan the 3-D structure of arbitrary objects (e.g. random packings of spheres) with a resolution of about 0.1 mm or better (magnetic resonance imaging, MRI) and to obtain information about the velocity of the fluid in selected planes of the same object. The combination of both methods allows for the first time with justifiable effort to investigate in 3-D and on a local level exactly the same arbitrarily complicated structures experimentally and numerically. This can be utilized first to validate the methods and results mutually, second to detect artifacts, but also third to replace or complement experimental investigations by “numerical experiments” on high performance computers which can provide a larger amount of detailed 3-D information with less effort.


Nuclear Magnetic Resonance Lattice Boltzmann Method Lattice Boltzmann Model Equilibrium Distribution Function High Performance Computer 
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  1. 1.
    J. Bernsdorf, G. Brenner, T. Zeiser, and P. Lammers. Perspectives of the lattice Boltzmann method for industrial applications. In C. Jenssen, T. Kvamdal, H. Andersson, B. Pettersen, A. Ecer, J. Periaux, N. Satofuka, and P. Fox, editors, Parallel Computational Fluid Dynamics 2000, Tends and Applications. Proceedings of the Parallel CFD 2000 Conference, May 22–25, Trondheim, Norway, pages 367–373. Elsevier, 2001.Google Scholar
  2. 2.
    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.MATHCrossRefGoogle Scholar
  3. 3.
    J. Bernsdorf, O. Günnewig, W. Hamm, and M. Münker. Strömungsberechnung in porösen Medien. GIT Labor-Fachzeitschrift, 4:387–390, 1999.Google Scholar
  4. 4.
    V. Bhandari. Detailed investigations of transport properties in complex reactor components. Master’s thesis, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, 2002.Google Scholar
  5. 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.MATHCrossRefGoogle Scholar
  6. 6.
    M. Bouzidi, M. Firdaouss, and P. Lallemand. Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids, 13(11):3452–3459, 2001.CrossRefGoogle Scholar
  7. 7.
    G. Brenner, T. Zeiser, and F. Durst. Simulation komplexer fluider Trans-portvorgänge in porösen Medien. Chem.-Ing.-Tech., 74(11):1533–1542, 2002.CrossRefGoogle Scholar
  8. 8.
    G. Brenner, T. Zeiser, P. Lammers, J. Bernsdorf, and F. Durst. Applications of lattice Boltzmann methods in CFD. ERCOFTAC bulletin, 50:29–34, 2001.Google Scholar
  9. 9.
    P. Callaghan. Principles of Nuclear Magnetic Resonance Microscopy. Clarendon, Oxford, 1991.Google Scholar
  10. 10.
    S. Chapman and T. G. Cowling. The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, 1995.Google Scholar
  11. 11.
    S. Chen and G. D. Doolen. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech., 30:329–364, 1998.CrossRefMathSciNetGoogle Scholar
  12. 12.
    F. Deserno, G. Hager, F. Brechtefeld, and G. Wellein. Performance of scientific applications on modern supercomputers. In S. Wagner, W. Hanke, A. Bode, and F. Durst, editors, High Performance Computing in Science and Engineering, Munich 2004, pages 3–25. Springer, 2004.Google Scholar
  13. 13.
    S. Donath. On optimized implementations of the lattice Boltzmann method on contemporary high performance architectures. Bachelor’s thesis, Chair of System Simulation, University of Erlangen-Nuremberg, Germany, 2004.Google Scholar
  14. 14.
    L. F. Gladden. Magnetic resonance: Ongoing and future role in chemical engineering research. AIChE Journal, 49(1):2–9, 2003.CrossRefGoogle Scholar
  15. 15.
    O. Filippova and D. Hänel. Grid refinement for lattice-BGK models. J. Comput. Phys., 147:219–228, 1998.MATHCrossRefGoogle Scholar
  16. 16.
    H. Freund, T. Zeiser, F. Huber, E. Klemm, G. Brenner, F. Durst, and G. Emig. Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation. Chem. Eng. Sci., 58(3–6):903–910, 2003.CrossRefGoogle Scholar
  17. 17.
    U. Frisch, D. d’Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivert. Lattice gas hydrodynamics in two and three dimensions. Complex Systems, 1:649–707, 1987.MATHMathSciNetGoogle Scholar
  18. 18.
    U. Frisch, B. Hasslacher, and Y. Pomeau. Lattice-gas automata for the Navier-Stokes Equation. Phys. Rev. Lett., 56(14):1505–1508, 1986.CrossRefGoogle Scholar
  19. 19.
    L.F. Gladden and P. Alexander. Application of nuclear magnetic resonance imaging in process engineering. Meas. Sci. Technol., 7:423–435, 1996.CrossRefGoogle Scholar
  20. 20.
    J. Hardy, O. de Pazzis, and Y. Pomeau. Molecular dynamics of a classical gas: Transport properties and time correlation functions. Phys. Rev. A, 13(5):1949–1961, 1976.CrossRefGoogle Scholar
  21. 21.
    X. He and L.-S. Luo. Lattice Boltzmann model for the incompressible Navier-Stokes equation. J. Stat. Phys., 88(3/4):927–944, 1997.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    X. He and L.-S. Luo. A priori derivation of the lattice Boltzmann equation. Phys. Rev. E, 55(6):R6333–R6336, 1997.CrossRefGoogle Scholar
  23. 23.
    X. He and L.-S. Luo. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E, 56(6):6811–6817, 1997.CrossRefGoogle Scholar
  24. 24.
    C. Heinen. MRI Untersuchungen zur Strömung newtonscher wad nicht-newtonscher Fluide in porösen Strukturen. PhD thesis, Universtität Karlsruhe (TH), 2004.Google Scholar
  25. 25.
    T. Inamuro, M. Yoshino, and F. Ogino. A non-slip boundary condition for lattice Boltzmann simulations. Phys. Fluids, 7(12):2928–2930, 1995.MATHCrossRefGoogle Scholar
  26. 26.
    M. Krafczyk, J. Tölke, and L.-S. Luo. Large-eddy simulations with a multiple-relaxation-time LBE model. Int. J. Mod. Phys. B, 17(1&2):33–40, 2003.CrossRefGoogle Scholar
  27. 27.
    A. Krischke. Modellierung und experimentelle Untersuchung von Transport-prozessen in durchströmten Schüttungen, volume 713 of VDI Fortschritt-Berichte, Reihe 3. VDI-Verlag, Düsseldorf, 2001.Google Scholar
  28. 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.MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    W. B. Lindquist. 3DMA-Rock. Scholar
  30. 30.
    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
  31. 31.
    S. Succi. The Lattice Boltzmann Equation — For Fluid Dynamics and Beyond. Clarendon Press, 2001.Google Scholar
  32. 32.
    V. Vassilev. Analyse experimentell (mittels MRI/NMR) oder numerisch (durch LBM) ermittelter Geschwindigkeitsfelder poröser Strukturen. Bachelor’s thesis, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, 2003.Google Scholar
  33. 33.
    D.A. Wolf-Gladrow. Lattice-Gas Cellular Automata and Lattice Boltzmann Models, volume 1725 of Lecture Notes in Mathematics. Springer, Berlin, 2000.MATHGoogle Scholar
  34. 34.
    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.CrossRefGoogle Scholar
  35. 35.
    H. Yu, L.-S. Luo, and S. S. Girimaji. Scalar mixing and chemical reaction simulations using lattice Boltzmann method. Int. J. Comp. Eng. Sci., 3(1):73–87, 2003.CrossRefGoogle Scholar
  36. 36.
    T. Zeiser, M. Steven, H. Freund, P. Lammers, G. Brenner, F. Durst, and J. Bernsdorf. Analysis of the flow field and pressure drop in fixed bed reactors with the help of lattice Boltzmann simulations. Phil. Trans. R. Soc. Lond. A, 360(1792):507–520, 2002.MATHCrossRefGoogle Scholar
  37. 37.
    T. Zeiser, G. Wellein, G. Hager, S. Donath, F. Deserno, P. Lammers, and M. Wierse. Optimized lattice Boltzmann kernels as testbeds for processor performance. Technical report, Regionales Rechenzentrum Erlangen, May 2004.Google Scholar
  38. 38.
    T. Zeiser, G. Wellein, and P. Lammers. Is there still a need for tailored HPC systems or can we go with commodity off-the-shelf clusters — some comments based on performance measurements using a lattice Boltzmann flow solver. submitted to InSiDE, the German HPC Journal, 2004.Google Scholar
  39. 39.
    D. P. Ziegler. Boundary conditions for lattice Boltzmann simulations. J. Stat. Phys., 71(5/6):1171–1177, 1993.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Lehrstuhl für Strömungsmechanik (LSTM)Universität Erlangen-NürnbergErlangenGermany

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