Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Grid Refinement Model in Lattice Boltzmann Method for Stream Function-Vorticity Formulations

유동함수-와도 관계를 이용한 격자볼츠만 방법에서의 격자 세밀화 모델

  • 신명섭 (동양미래대학교 기계공학부)
  • Received : 2014.12.09
  • Accepted : 2015.02.26
  • Published : 2015.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

본 연구에서는 2차원 비압축성 유체 유동을 해석하기 위하여 격자 세밀화 모델을 적용한 격자볼츠만 방법(LBM)을 수치적으로 연구하였다. 일반적으로 유동해석에서 충분한 정확도를 얻기 위해서는 관심 있는 영역에서 격자가 세밀하게 구성되어야 한다. 그래서 본 연구에서는 유동함수-와도 공식을 적용한 LBM에 격자 세밀화 모델을 적용하여 유동해석을 수행하였다. 공동형상 유동에서의 기존의 신뢰성 있는 유동장 결과와의 비교를 통해 본 연구의 격자 세밀화 모델을 적용한 격자볼츠만 방법의 신뢰성과 유용성을 검토하였다.

Keywords

References

  1. Chen, S. and Doolen, G. D., 1998, "Lattice Boltzmann Method for Fluid Flows," Annual Review of Fluid Mechanics, Vol. 30, pp. 329-364. https://doi.org/10.1146/annurev.fluid.30.1.329
  2. Aidun, C. K. and Clausen, J. R., 2010, "Lattice-Boltzmann Method for Complex Flows," Annual Review of Fluid Mechanics, Vol. 42, pp. 439-472. https://doi.org/10.1146/annurev-fluid-121108-145519
  3. Chen, S., Tolke, J., and Krafczyk, M., 2008, "A New Method for the Numerical Solution of Vorticity-streamfunction Formulations," Computer Methods in Applied Mechanics and Engineering, Vol. 198, pp. 367-376. https://doi.org/10.1016/j.cma.2008.08.007
  4. Chen, S., 2009, "A Large-eddy-based Lattice Boltzmann Model for Turbulent Flow Simulation," Applied Mathematics and Computation, Vol. 215, pp. 591-598. https://doi.org/10.1016/j.amc.2009.05.040
  5. Filippova, D. and Hanel, D., 1998, "Grid Refinement for Lattice-BGK Models," Journal of Computational physics, Vol. 147, pp. 219-228. https://doi.org/10.1006/jcph.1998.6089
  6. Lin, C.L. and Lai, Y., 2000, "Lattice Boltzmann Method on Composite Grids," Physical Review E, Vol. 62, pp. 2219-2225. https://doi.org/10.1103/PhysRevE.62.2219
  7. Yu, D., Mei, R. and Shyy, W., 2002, "A Multi-block Lattice Boltzmann Method for Viscous Fluid Flows," International Journal for Numerical Methods in Fluids, Vol. 39, pp. 99-120. https://doi.org/10.1002/fld.280
  8. Dupuis, A. and Chopard, B., 2003, "Theory and Applications of an Alternative Lattice Boltzmann Grid Refinement Algorithm," Physical Review E, Vol. 67, 066707. https://doi.org/10.1103/PhysRevE.67.066707
  9. Chai, Z. and Shi, B., 2008, "A Novel Lattice Boltzmann Model for the Poisson Equation," Applied Mathematical Modelling, Vol. 32, pp. 2050-2058. https://doi.org/10.1016/j.apm.2007.06.033
  10. Shankar, P. N. and Deshpande, M. D., 2000, "Fluid Mechanics in the Driven Cavity," Annual Review of Fluid Mechanics, Vol. 32, pp. 93-136. https://doi.org/10.1146/annurev.fluid.32.1.93
  11. Ghia, U., Ghia, K. N. and Shin, C. T., 1982, "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method," Journal of Computational Physics, Vol. 48, pp. 387-411. https://doi.org/10.1016/0021-9991(82)90058-4
  12. Hou, S., Zou, Q., Chen, S., Doolen, G. and Cogley, A. C., 1995, "Simulation of Cavity Flow by Lattice Boltzmann Method," Journal of Computational Physics, Vol. 118, pp. 329-347. https://doi.org/10.1006/jcph.1995.1103
  13. Gupta, M. M. and Kalita J. C., 2005, "A New Paradigm for Solving Navier-Stokes Equations: Streamfunction-velocity Formulation," Journal of Computational Physics, Vol. 207, pp. 52-68. https://doi.org/10.1016/j.jcp.2005.01.002
  14. Shin., M. S., Jeon, S. Y. and Yoon, J. Y., 2013, "Numerical Investigation of Mixing Characteristics in a Cavity Flow by Using Hybrid Lattice Boltzmann Method," Trans. Korean Soc. Mech. Eng. B, Vol. 37, No. 7, pp. 683-693. https://doi.org/10.3795/KSME-B.2013.37.7.683
  15. Benjamin, A. S. and Denny, V. E., 1979, "On the Convergence of Numerical Solutions for 2-D Flows in a Cavity at Large Re," Journal of Computational physics, Vol. 33, pp. 340-358. https://doi.org/10.1016/0021-9991(79)90160-8