Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-18T15:36:01.877Z Has data issue: false hasContentIssue false
  • English
  • Français

A finite-volume gas-kinetic method for the solution of the Navier-Stokes equations

Published online by Cambridge University Press:  27 January 2016

M. Righi
M. Righi*
Affiliation:
Zurich University of Applied Sciences, Winterthur, Switzerland
*
rigm@zhaw.ch
Get access Rights & Permissions [Opens in a new window]

Abstract

Gas-kinetic theory is also valid in the continuum regime: the Euler and Navier-Stokes equations can be obtained as projection of the Boltzmann equation on to the physical space (x,t). The numerical schemes derived from gas-kinetic theory are computationally more expensive than Navier-Stokes based ones, but offer advantages which have been attracting a growing level of attention: they can (i) accommodate discontinuities at cells interface, (ii) provide high-resolution fluxes, (iii) provide advantages in the simulation of turbulence, (iv) handle hypersonic and/or rarefied flows. This study extends the validation of gas-kinetic schemes investigating a few turbulent flow cases. At a slightly higher computational cost, gas-kinetic schemes provide results comparable to those obtained with well-validated Navier-Stokes schemes using the same turbulence model, grid and reconstruction order. In the case of shock-separated flows, the results obtained with the gas-kinetic scheme are even closer to experimental data. These findings are consistent with the idea that gas-kinetic theory is a physically more consistent framework for investigating the mechanics of fluids.

Type
Research Article
Information
The Aeronautical Journal , Volume 117 , Issue 1192 , June 2013 , pp. 605 - 616
Copyright
Copyright © Royal Aeronautical Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Cercignani, C. The Boltzmann equation and its applications, 1988, 67, Springer.Google Scholar
2. Godunov, S. Math. Sbornik 89, 1959, pp 271–306.Google Scholar
3. Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S. and Yakhot, V. Science, 2003, 301, pp 633–636.Google Scholar
4. Chen, H., Orszag, S., Staroselsky, I. and Succi, S. J Fluid Mech, 2004, 519, pp 301–314.Google Scholar
5. Righi, M. A gas-kinetic scheme for the simulation of turbulent flows, Rarefied Gas Dynamics, 2012.Google Scholar
6. Xu, K. J Comput Phys, 2001, 171, pp 289–335.Google Scholar
7. May, G. Srinivasan, B. and Jameson, A. J Comput Phys, 2007, 220, pp 856–878.Google Scholar
8. Tang, L. Comput Fluids, 2012, 56, pp 39–48.Google Scholar
9. Mandal, J. and Deshpande, S. Comput Fluids, 1994, 23, pp 447–478.Google Scholar
10. Chou, S. and Baganoff, D. J Comput Phys, 1997, 130, pp 217–230.Google Scholar
11. Xu, K. and K., Prendergast, J Comput Phys, 1994, 114, pp 9–17.Google Scholar
12. Bhatnagar, P., Gross, E. and Krook, M. Phys Rev, 1954, 94, p 511.Google Scholar
13. Jameson, A. Schmidt, W. Turkel, E. et al, AIAA paper, 1981, 81, p 9.Google Scholar
14. Wilcox, D. C. Turbulence Modeling for CFD, Third edition, 2006, DCW Industries, La Canada, CA, USA.Google Scholar
15. Yoon, S. and Jameson, A. AIAA J, 1988, 26, pp 1025–1026.Google Scholar
16. Jameson, A. Appl Math Comput, 1983, 13, pp 327–356.Google Scholar
17. Xu, K., Mao, M. and Tang, L. J Comput Phys, 2005, 203, pp 405–421.Google Scholar
18. Lee, H. and Huang, R. J Marine Science and Technology, 1998, 6, pp 29–37.Google Scholar
19. Jiang, G. and Shu, C. Efficient implementation of weighted eno schemes, 1995, Tech report, DTIC Document.Google Scholar
20. Liu, X., Osher, S. and Chan, T. J Comput Phys, 1994, 115, pp 200–212.Google Scholar
21. Li, Q., Xu, K. and Fu, S. J Comput Physics, 2010, 229, pp 6715–6731.Google Scholar
22. Cook, P., McDonald, M. and Firman, M. AGARD Advisory, 1979.Google Scholar
23. Harris, C. NASA Technical Memorandum, 1981.Google Scholar
24. Wallin, S. and Johansson, A. J Fluid Mech, 2000, 403, pp 89–132.Google Scholar
25. Johnson, D., Bachalo, W. and Owen, F. NASA Technical Memorandum, 1981.Google Scholar