Parallel unstructured finite volume lattice Boltzmann method for high-speed viscid compressible flows
Abstract
Based on the double distribution function Boltzmann-BGK equations, a cell-centered finite volume lattice Boltzmann method on unstructured grids for high-speed viscid compressible flows is presented. In the equations, the particle distribution function is introduced on the basis of the D2Q17 circular function, and its corresponding total energy distribution function is adopted. In the proposed method, the advective term is evaluated by Roe’s flux-difference splitting scheme, and a limiter is used to prevent the generation of oscillations. The distribution functions on the interface are calculated by piecewise linear reconstruction, in which the gradient is computed by the least-squares approach. In order to do large-scale simulations, a parallel algorithm is illustrated. The present method is validated by a flow around the NACA0012 airfoil and a flow past a circular cylinder at high Mach numbers. The results agree well with the published results, which demonstrate that the present method is an efficient numerical method for high-speed viscid compressible flows. The parallel performance results show that the proposed parallel algorithm achieves 90% parallel efficiency on 4800 cores for a problem with unstructured triangle cells, which shows the potential to perform fast and high-fidelity simulations of large-scale high-speed viscid compressible flows in complicated computational domains.
References
- 1. , Lattice Boltzmann method and its Applications in Engineering (World Scientific, 2013). Link, Google Scholar
- 2. , The Lattice Boltzmann Equations for Complex States of Flowing Matter (Oxford University Press, 2018). Crossref, Google Scholar
- 3. , Int. J. Mod. Phys. C 31, 2050173 (2020). Link, Web of Science, ADS, Google Scholar
- 4. , SIAM J. Sci. Comput. 37, S291 (2015). Crossref, Web of Science, Google Scholar
- 5. , Comput. Fluids 105, 58 (2014). Crossref, Web of Science, Google Scholar
- 6. , Phys. Fluids 30, 040903 (2018). Crossref, Web of Science, Google Scholar
- 7. , Int. J. Heat Mass Transf. 160, 120156 (2020). Crossref, Web of Science, Google Scholar
- 8. , J. Stat. Phys. 68, 401 (1992). Crossref, Web of Science, ADS, Google Scholar
- 9. , Phys. Rev. E 59, 4675 (1999). Crossref, Web of Science, ADS, Google Scholar
- 10. , Phys. Rev. E 59, 6202 (1999). Crossref, Web of Science, ADS, Google Scholar
- 11. , Phys. Rev. E 68, 016701 (2003). Crossref, Web of Science, ADS, Google Scholar
- 12. , Int. J. Numer. Methods Fluids 49, 619 (2005). Crossref, Web of Science, Google Scholar
- 13. , Comput. Fluids 35, 814 (2006). Crossref, Web of Science, Google Scholar
- 14. , J. Comput. Phys. 228, 5262 (2009). Crossref, Web of Science, ADS, Google Scholar
- 15. , Commun. Comput. Phys. 20, 301 (2016). Crossref, Web of Science, ADS, Google Scholar
- 16. , J. Comput. Phys. 327, 503 (2016). Crossref, Web of Science, ADS, Google Scholar
- 17. , Phys. Rev. E 101, 063301 (2020). Crossref, Web of Science, ADS, Google Scholar
- 18. , Phys. Rev. E 47, R2249 (1993). Crossref, Web of Science, ADS, Google Scholar
- 19. , J. Sci. Comput. 8, 231 (1993). Crossref, Google Scholar
- 20. , Phys. Rev. E 50, 2776 (1994). Crossref, Web of Science, ADS, Google Scholar
- 21. , Phys. Rev. E 67, 036306 (2003). Crossref, Web of Science, ADS, Google Scholar
- 22. , Int. J. Numer. Methods Fluids 55, 41 (2007). Crossref, Web of Science, Google Scholar
- 23. , Phys. Rev. E 58, 7283 (1998). Crossref, Web of Science, ADS, Google Scholar
- 24. , Phys. Rev. E 61, 2645 (2000). Crossref, Web of Science, ADS, Google Scholar
- 25. , J. Comput. Phys. 146, 282 (1998). Crossref, Web of Science, ADS, Google Scholar
- 26. , Phys. Rev. E 69, 056702 (2004). Crossref, Web of Science, ADS, Google Scholar
- 27. , Eur. Phys. Lett. 90, 54003 (2010). Crossref, Web of Science, ADS, Google Scholar
- 28. , Phys. Lett. A 375, 2129 (2011). Crossref, Web of Science, ADS, Google Scholar
- 29. , Phys. Rev. E 75, 036706 (2007). Crossref, Web of Science, ADS, Google Scholar
- 30. K. Qu, Ph.D. thesis, Development of Lattice Boltzmann Method for Compressible Flows (National University of Singapore, 2008). Google Scholar
- 31. , Phys. Rev. E 76, 056705 (2007). Crossref, Web of Science, ADS, Google Scholar
- 32. , Phys. Lett. A 373, 2101 (2009). Crossref, Web of Science, ADS, Google Scholar
- 33. , Int. J. Numer. Methods Fluids 77, 334 (2015). Crossref, Web of Science, ADS, Google Scholar
- 34. , Chin. Phys. B 24, 050501 (2015). Crossref, Web of Science, Google Scholar
- 35. , Comput. Fluids 166, 24 (2018). Crossref, Web of Science, Google Scholar
- 36. , Phys. Rev. E 75, 036704 (2007). Crossref, Web of Science, ADS, Google Scholar
- 37. , Phys. Rev. E 103, 023306 (2020). Crossref, Web of Science, Google Scholar
- 38. , Int. J. Parallel Program. 37, 593 (2009). Crossref, Web of Science, Google Scholar
- 39. , Comput. Fluids 39, 1411 (2010). Crossref, Web of Science, Google Scholar
- 40. , Parallel Comput. 37, 521 (2011). Web of Science, Google Scholar
- 41. , Parallel Comput. 39, 259 (2013). Crossref, Web of Science, Google Scholar
- 42. , Comput. Fluids 110, 1 (2015). Crossref, Web of Science, Google Scholar
- 43. G. Karypis and K. Schloegel, ParMETIS: Parallel graph partitioning and sparse matrix ordering library version 4.0, University of Minnesota (2013). Google Scholar
- 44. S. Balay, S. Abhyankar, M. F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin, A. Dener, V. Eijkhout, W. D. Gropp, D. Karpeyev, D. Kaushik, M. G. Knepley, D. May, L. C. McInnes, R. T. Mills, T. Munson, K. Rupp, P. Sanan, B. F. Smith, S. Zampini, H. Zhang and H. Zhang, PETSc Users Manual, Argonne National Laboratory (2020). Google Scholar
- 45. , J. Comput. Phys. 43, 250 (1981). Crossref, Web of Science, Google Scholar
- 46. , J. Comput. Phys. 118, 120 (1995). Crossref, Web of Science, ADS, Google Scholar
- 47. , Comput. Math. App. 79, 1590 (2019). Web of Science, Google Scholar
- 48. . Computational Fluid Dynamics: Principles and Applications (Elsevier, 2015). Google Scholar
- 49. , The finite volume method in computational fluid dynamics: An advanced introduction with OpenFOAM and Matlab (Springer, 2016). Crossref, Google Scholar
- 50. , Chin. Phys. 11, 366 (2002). Crossref, ADS, Google Scholar
- 51. , J. Comput. Phys. 131, 267 (1997). Crossref, Web of Science, ADS, Google Scholar
- 52. , J. Comput. Phys. 225, 2098 (2007). Crossref, Web of Science, ADS, Google Scholar
- 53. , Comput. Fluids 26, 249 (1997). Crossref, Web of Science, Google Scholar
- 54. , Int. J. Mod. Phys. C 19, 1581 (2008). Link, Web of Science, ADS, Google Scholar
- 55. , Front. Comput. Sci. 8, 345 (2014). Crossref, Web of Science, Google Scholar
- 56. , Parallel Scientific Computing (Wiley, 2016). Google Scholar
You currently do not have access to the full text article. |
---|