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Kinetic Modeling and Simulation of Environmental and Civil Engineering Flow Problems

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100 Volumes of ‘Notes on Numerical Fluid Mechanics’

Summary

In this contribution the authors address recent advances of modelling and simulating flow problems related to Environmental and Civil Engineering using Lattice-Boltzmann methods (LBM) and present results documenting the potential of this kinetic approach. After a short introduction to theoretical aspects of the method, we address extensions of the basic LB ansatz to model turbulent, thermal and multiphase flows, free surface flows and bidirectional Fluid-Structure-Interaction. All simulations were done with the LBM research prototype software Virtual Fluids [16], a transient 2D/3Dcode offering adaptive hierarchical Cartesian grid refinement, massive parallelization and multi-physics capabilities. The simulation of a simplified debris flow problem is based on the coupling of the flow solver with an external physics engine.

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References

  1. Ahrenholz, B., Tölke, J., Krafczyk, M.: Lattice-Boltzmann simulations in reconstructed parameterized porous media. International Journal of Computational Fluid Dynamics 20(6), 369–377 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahrenholz, B., Tölke, J., Lehmann, P., Peters, A., Kaestner, A., Krafczyk, M., Durner, W.: Prediction of capillary hysteresis in porous material using lattice Boltzmann methods and comparison to experimental data and a morphological pore network model. Advances in Water Resources (acc. for publ., 2008)

    Google Scholar 

  3. Ansumali, S., Karlin, I., Succi, S.: Kinetic theory of turbulence modeling: smallness parameter, scaling and derivation of smagorinsky model. Physica A 338(3-4), 379 (2004)

    Article  MathSciNet  Google Scholar 

  4. Benzi, R., Succi, S., Vergassola, M.: The lattice Boltzmann equation: theory and applications. Physics Reports 222(3), 147–197 (1992)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Bouzidi, M., Firdaouss, M., Lallemand, P.: Momentum transfer of a Boltzmann-Lattice fluid with boundaries. Physics of Fluids 13(11), 3452–3459 (2001)

    Article  Google Scholar 

  7. Bungartz, H.J., Schäfer, M. (eds.): Fluid-Structure Interaction, Modelling, Simulation and Optimisation. Lecture Notes in Computational Science and Engineering, vol. 53. Springer, Heidelberg (2006)

    Google Scholar 

  8. Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge (1990)

    Google Scholar 

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

    Article  Google Scholar 

  10. Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics 30, 329–364 (1998)

    Article  MathSciNet  Google Scholar 

  11. Crouse, B., Rank, E., Krafczyk, M., Tölke, J.: A LB-based approach for adaptive flow simulations. International Journal of Modern Physics B 17, 109–112 (2002)

    Article  Google Scholar 

  12. d’Humières, D.: Generalized lattice-Boltzmann equations. In: Shizgal, B.D., Weave, D.P. (eds.) Rarefied Gas Dynamics: Theory and Simulations, Washington DC. Prog. Astronaut. Aeronaut, vol. 159, pp. 450–458. AIAA (1992)

    Google Scholar 

  13. d’Humières, D., Ginzburg, I., Krafczyk, M., Lallemand, P., Luo, L.-S.: Multiple-relaxation-time lattice Boltzmann models in three-dimensions. In: Philosophical Transactions of the Royal Society A-Mathematical, Physical and Engineering Sciences, vol. 360, pp. 437–451 (2002)

    Google Scholar 

  14. Feng, Y.T., Han, K., Owen, D.R.J.: Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues. International Journal for Numerical Methods in Engineering 72(9), 1111–1134 (2007)

    Article  MathSciNet  Google Scholar 

  15. Filippova, O., Hänel, D.: A novel lattice BGK approach for low Mach number combustion. Journal of Computational Physics 158, 139 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Freudiger, S., Hegewald, J., Krafczyk, M.: A parallelization concept for a multi-physics lattice Boltzmann prototype based on hierarchical grids. Progress in Computational Fluid Dynamics (in press, 2008)

    Google Scholar 

  17. Geller, S., Krafczyk, M., Tölke, J., Turek, S., Hron, J.: Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite volume Methods for laminar Flows. Computers & Fluids 35, 888–897 (2006)

    Article  Google Scholar 

  18. Geller, S., Tölke, J., Krafczyk, M.: Lattice-Boltzmann Method on quadtree type grids for Fluid-Structure-Interaction. In: Bungartz, H.-J., Schäfer, M. (eds.) Fluid-Structure Interaction:Modelling, Simulation, Optimisation. Lecture Notes in Computational Science and Engineering, vol. 53. Springer, Heidelberg (2006)

    Google Scholar 

  19. Ginzburg, I.: Equilibrium type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Advances in Water Resources 28(11), 1171–1195 (2005)

    Article  Google Scholar 

  20. Ginzburg, I.: Lattice Boltzmann modeling with discontinuous collision components: Hydrodynamic and advection-diffusion equations. Journal of Statistical Physics 126, 157–206 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Ginzburg, I., d’Humières, D.: Multireflection boundary conditions for lattice Boltzmann models. Physical Review E 68, 066614 (2003)

    Article  Google Scholar 

  22. Ginzburg, I., Steiner, K.: Lattice Boltzmann model for free-surface flow and its application to filling process in casting. Journal of Computational Physics 185, 61–99 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ginzburg, I., Verhaeghe, F., d’Humières, D.: Two-relaxation-time lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions. Communications in Computational Physics 3, 427–478 (2008)

    MathSciNet  Google Scholar 

  24. Gunstensen, A.K., Rothman, D.: Lattice Boltzmann modell of immiscible fluids. Physical Review A 43(8), 4320–4327 (1991)

    Article  Google Scholar 

  25. He, X., Chen, S., Doolen, G.D.: A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit. Journal of Computational Physics 146, 282 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  26. He, X., Luo, L.-S.: Lattice Boltzmann model for the incompressible Navier-Stokes equation. Journal of Statistical Physics 88(3-4), 927–944 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hübner, B., Walhorn, E., Dinkler, D.: A monolithic approach to fluid-structure interaction using space-time finite elements. Computer Methods in Applied Mechanics and Engineering 193(23–26), 2087–2104 (2004)

    Article  MATH  Google Scholar 

  28. Iglberger, K.: PE - Physics Engine (2008), http://www10.informatik.uni-erlangen.de/de/~klaus/

  29. Janssen, C.: Simulation von Strömungen mit freien Oberflächen auf blockstrukturierten Gittern mit der Lattice Boltzmann Methode. iRMB, TU Braunschweig (2007)

    Google Scholar 

  30. Junk, M., Klar, A., Luo, L.S.: Asymptotic analysis of the lattice Boltzmann equation. Journal of Computational Physics 210, 676 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kaestner, A., Lehmann, E., Stampanoni, M.: Applications of Imaging and Image Processing in Soil Science. Advances in Water Resources (acc. for publ., 2008)

    Google Scholar 

  32. Krafczyk, M., Tölke, J., Luo, L.-S.: Large-eddy simulations with a multiple-relaxation-time LBE model. International Journal of Modern Physics C 17(1-2), 33–39 (2003)

    Google Scholar 

  33. Krafczyk, M., Tölke, J., Rank, E., Schulz, M.: Two-dimensional simulation of fluid-structure interaction using lattice-Boltzmann methods. Computers & Structures 79, 2031–2037 (2001)

    Article  Google Scholar 

  34. Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability. Physical Review E 61(6), 6546–6562 (2000)

    Article  MathSciNet  Google Scholar 

  35. Lallemand, P., Luo, L.-S.: Lattice Boltzmann method for moving boundaries. Journal of Computational Physics 184, 406–421 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  36. Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: Acoustic and thermal properties. Physical Review E 68, 036706 (2003)

    Article  MathSciNet  Google Scholar 

  37. Mezrhab, A., Bouzidi, M., Lallemand, P.: Hybrid lattice-Boltzmann finite-difference simulation of convective flows. Computers & Fluids 33, 623–641 (2004)

    Article  MATH  Google Scholar 

  38. Pan, C., Hilpert, M., Miller, C.T.: Lattice-Boltzmann simulation of two-phase flow in porous media. Water Resources Research 40 (2004)

    Google Scholar 

  39. Pavlo, P., Vahala, G., Vahala, L.: Preliminary Results in the Use of Energy-Dependent Octagonal Lattices for Thermal Lattice Boltzmann Simulations. Journal of Statistical Physics 107, 499 (2002)

    Article  MATH  Google Scholar 

  40. Prosperetti, A., Tryggvason, G. (eds.): Computational Methods for Multiphase Flow. Cambridge University Press, Cambridge (2006)

    Google Scholar 

  41. Qian, Y.H., d’Humières, D., Lallemand, P.: Lattice BGK models for Navier-Stokes equation. Europhysics Letters 17, 479–484 (1992)

    Article  MATH  Google Scholar 

  42. Rheinländer, M.: A Consistent Grid Coupling Method for Lattice-Boltzmann Schemes. Journal of Statistical Physics 121, 49–74 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  43. Shan, X.: Simulation of Rayleigh-Bernard convection using the lattice Boltzmann method. Physical Review E 55, 2780 (1997)

    Article  Google Scholar 

  44. Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E 47, 1815–1819 (1993)

    Article  Google Scholar 

  45. Shi, X., Lim, S.P.: A LBM-DLM/FD method for 3D fluid-structure interactions. Journal of Computational Physics 226(2), 2028–2043 (2007)

    Article  MATH  Google Scholar 

  46. Shi, X., Phan-Thien, N.: Distributed Lagrange multiplier/fictitious domain method in the framework of lattice Boltzmann method for fluid-structure interactions. Journal of Computational Physics 206(1), 81–94 (2005)

    Article  MATH  Google Scholar 

  47. Stiebler, M., Tölke, J., Krafczyk, M.: An Advection-Diffusion Lattice Boltzmann Scheme for Hierarchical Grids. Computers & Mathematics with Applications 55(7), 1576–1584 (2007)

    Article  Google Scholar 

  48. Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, Oxford (2001)

    MATH  Google Scholar 

  49. Sun, C.: Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties. Physical Review E 61, 2645 (2000)

    Article  Google Scholar 

  50. Swift, M.R., Osborn, W.R., Yeomans, J.M.: Lattice Boltzmann simulation of nonideal fluids. Physical Review Letters 75(5), 830–833 (1995)

    Article  Google Scholar 

  51. Teixeira, C.M.: Incorporating turbulence models into the lattice-Boltzmann method. International Journal of Modern Physics C 9(8), 1159–1175 (1998)

    Article  MathSciNet  Google Scholar 

  52. Thürey, N., Rüde, U.: Stable free surface flows with the lattice Boltzmann method on adaptively coarsened grids. cvs (preprint, 2008)

    Google Scholar 

  53. Tölke, J.: A thermal model based on the lattice Boltzmann method for low Mach number compressible flows. Journal of Computational and Theoretical Nanoscience 3(4), 579–587 (2006)

    Google Scholar 

  54. Tölke, J.: TeraFLOP Computing on a Desktop PC with GPUs for 3D CFD. International Journal of Computational Fluid Dynamics (acc. for publ., 2008)

    Google Scholar 

  55. Tölke, J., Freudiger, S., Krafczyk, M.: An adaptive scheme for LBE multiphase flow simulations on hierarchical grids. Computers & Fluids 35, 820–830 (2006)

    Article  Google Scholar 

  56. Tölke, J., Krafczyk, M., Schulz, M., Rank, E.: Lattice Boltzmann Simulations of binary fluid flow through porous media. Philosophical Transactions of the Royal Society A-Mathematical, Physical and Engineering Sciences 360(1792), 535–545 (2002)

    Article  MATH  Google Scholar 

  57. Tryggvason, G., Esmaeeli, A., Homma, S., Lu, J., Biswas, S.: Recent Progress in Computational Studies of Disperse Bubbly Flows. Multiphase Flow Science and Technology 18, 231–249 (2006)

    Article  Google Scholar 

  58. Turek, S., Hron, J.: Proposal for Numerical Benchmarks for Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow. In: Bungartz, H.-J., Schäfer, M. (eds.) Fluid-Structure Interaction, Modelling, Simulation and Optimisation. Lecture Notes in Computational Science and Engineering, vol. 53, pp. 371–385. Springer, Heidelberg (2006)

    Google Scholar 

  59. Vahala, L., Wah, D., Vahala, G., Carter, J., Pavlo, P.: Thermal Lattice Boltzmann Simulation for Multispecies Fluid Equilibration. Physical Review E 62, 507 (2000)

    Article  Google Scholar 

  60. van Treeck, C., Rank, E., Krafczyk, M., Tölke, J., Nachtwey, B.: Extension of a hybrid thermal LBE scheme for Large-Eddy simulations of turbulent convective flows. Computers & Fluids 35(8–9), 863–871 (2006)

    Google Scholar 

  61. Walhorn, E., Kölke, A., Hübner, B., Dinkler, D.: Fluid-structure coupling within a monolithic model involving free surface flows. Computers & Structures 83(25–26), 2100–2111 (2005)

    Article  Google Scholar 

  62. Wall, W.A., Genkinger, S., Ramm, E.: A strong coupling partitioned approach for fluid-structure interaction with free surfaces. Computers & Fluids 36(1), 169–183 (2007)

    Article  MATH  Google Scholar 

  63. Yu, D., Mei, R., Luo, L.-S., Shyy, W.: Viscous flow computations with the method of lattice Boltzmann equation. Progress in Aerospace Sciences 39, 329–367 (2003)

    Article  Google Scholar 

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Krafczyk, M. et al. (2009). Kinetic Modeling and Simulation of Environmental and Civil Engineering Flow Problems. In: Hirschel, E.H., Krause, E. (eds) 100 Volumes of ‘Notes on Numerical Fluid Mechanics’. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70805-6_26

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  • DOI: https://doi.org/10.1007/978-3-540-70805-6_26

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