Numerical Analysis of a Weak Shock Wave Propagating in a Medium Using Lattice Boltzmann Method (LBM)

  • Kang, Ho-Keun ;
  • Michihisa Tsutahara (Graduate School of Science and Technology, Kobe University) ;
  • Ro, Ki-Deok (School of Mechanical and Aerospace Engineering·Institute of Marine Industry, Gyeongsang National University) ;
  • Lee, Young-Ho (Division of Mechanical & Information Engineering, Korea Maritime University)
  • 발행 : 2003.12.01

초록

This study introduced a lattice Boltzmann computational scheme capable of modeling thermo hydrodynamic flows with simpler equilibrium particle distribution function compared with other models. The equilibrium particle distribution function is the local Maxwelian equilibrium function in this model, with all the constants uniquely determined. The characteristics of the proposed model is verified by calculation of the sound speeds, and the shock tube problem. In the lattice Boltzmann method, a thermal fluid or compressible fluid model simulates the reflection of a weak shock wave colliding with a sharp wedge having various angles $\theta$$\sub$w/. Theoretical results using LBM are satisfactory compared with the experimental result or the TVD.

키워드

참고문헌

  1. Alexander, F. J., Chen, S. and Sterling, D. J., 1993, 'Lattice Boltzmann thermodynamics,' Physical Review E, Vol. 47, pp. 2249-2252 https://doi.org/10.1103/PhysRevE.47.R2249
  2. Chen, H., Chen, S. and Matthaeus, W. H., 1992, 'Recovery of the Navier-Stokes Equations Using a Lattice-Gas Boltzmann Method,' Physical Review A, Vol. 45, pp. R5339-5342 https://doi.org/10.1103/PhysRevA.45.R5339
  3. Chen, Y., Ohashi, H. and Akiyama, M., 1994, 'Thermal Lattice Bhatnagar Gross Krook Model without Nonlinear Deviations in Macrodynamic Equations,'Physical-Review E, Vol. 50,pp. 2776-2783 https://doi.org/10.1103/PhysRevE.50.2776
  4. Cornubert, R., d'Humiere, D. and Levermoer, D., 1991, 'A Knudsen layer theory for lattice gases,' Physica D, Vol. 47, pp. 241-259 https://doi.org/10.1016/0167-2789(91)90295-K
  5. Frisch, U., Hasslacher, B. and Pomeau, Y., 1986, 'Lattice-Gas Automata for the Navier-Stokes Equation,' Physical Review Letters, Vol. 55, pp.1505-1508
  6. Gabie, B. D., 1992, 'Shock Wave Reflection Phenomena,' Springer Verlag
  7. McNamara, G. and Zannetti, G., 1988, 'Use of the Boltzmann Equation to Simulate Lattice Gas Automata,' Physical Review Letters, Vol. 61, pp.2332-2335 https://doi.org/10.1103/PhysRevLett.61.2332
  8. Qain, Y. H., D'Humieres, D. and Lallemand, P., 1992, 'Lattice BGK models for Navier-Stokes Equation,' Europhysis Letters, Vol. 17, pp. 479-484 https://doi.org/10.1209/0295-5075/17/6/001
  9. Rothman, D. H. and Zaleski, S., 1997, 'Lattice-Gas Celluar Automata-Simple Models of Complex Hydrodynamics,' Cambridge University Press
  10. Sasoh, A., Takayama, K. and Saito, T., 1992, 'A weak shock wave reflection over wedge,' Shock Waves 2, pp.277-281 https://doi.org/10.1007/BF01414764
  11. Tsutahara, M. and Kang, H. K., 2002, 'A Discrete Effect of the Thermal Lattice BGK Model,' Journal of Statistical Physics, Vol. 107, No. 112, pp. 479-498. c https://doi.org/10.1023/A:1014591527900
  12. Wolf-Gladrow, D. A., 2000, 'Lattice-gas Cellular Automata and Lattice Boltzmann Models,' Lecture Notes in Mathematics, Springer. Ms