ANZIAM J. 46(E) pp.C1371--C1414, 2006.

High performance computation for direct numerical and large eddy simulation

Chaoqun Liu
(Received 18 November 2004, revised 25 February 2006)

Abstract

This paper focusses on high order compact schemes for direct numerical simulation (DNS) and large eddy simulation (LES) for flow separation, transition, tip vortex, and flow control. We discuss the fundamental issues of high quality grid generation, high order schemes for curvilinear coordinates, the CFL condition for complex geometry, and high-order weighted compact schemes for shock capturing and shock-vortex interaction. The computation examples include DNS for K-type and H-type transition, DNS for flow separation and transition around an airfoil with attack angle, control of flow separation by using pulsed jets, and LES simulation for a tip vortex behind the juncture of a wing and flat plate. Computations also show the almost linear growth in efficiency obtained using multiple processors.

Download to your computer

Authors

Chaoqun Liu
Department of Mathematics, University of Texas at Arlington, TX, USA. mailto:cliu@uta.edu

Published March 31, 2006. ISSN 1446-8735

References

  1. Boiko, A. V., Grek, G. R., Dovgal, A. V., Kozlov, V. V., The origin of turbulence in near-wall flows, pages 167--196, Springer, 2002.
  2. Bons, J. P., Sondergarrd, R., and Rivir, R. B., Turbine separation control using pulsed vortex generator jets, Journal of Turbomachinery, Vol. 123, pages 198--206, 2001.
  3. Chow, J. S., Zilliac, G. G., Bradshaw, P., Mean and turbulence mearements in the near field of a wingtip vortex, AIAA J. Vol. 35, 1561--1567, 1997.
  4. Ducros, F., Comte, P., and Lesieur, M., Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate, J. Fluid Mech, Vol. 1, 1996.
  5. Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. R., Uniformly high order accurate essential non-oscillatory schemes, III, Journal of Computational Physics, Vol. 71, pages 231--303, 1987.
  6. Herbert, T., Three-dimensional phenomena in the transitional flat-plate boundary layer, AIAA paper, 1985-0489, 1985.
  7. Jiang, G. S., Shu, C. W., Efficient implementation of weighted ENO scheme, J. Comput. Phys., Vol. 126, pages 202--228, 1996.
  8. Jiang, L., Choudari, M., Chang, C. and Liu, C., Direct numerical simulations of crossflow disturbances in supersonic boundary layers, Journal of Mathematics and Computers in Simulation, Vol. 65, pp 469-487, 2004.
  9. Jiang, L., Shan, H., and Liu, C., Weighted Compact Scheme for Shock Capturing, International Journal of Computational Fluid Dynamics, Vol. 15, pages 147--155, 2001.
  10. Jiang, L., Shan, H., Liu, C., and Visbal, M., Non-reflecting boundary conditions for dns in curvilinear coordinates, Recent Advances in dns and les, Proceedings of the Second AFOSR (Air Force Office of Scientific Research) International Conference, Rutgers, New Jersey, June 7-9, 1999.
  11. Kachanov, Yu. S. and Levchenko, V. Ya., Nonlinear development of a wave in a boundary layer Fluid Dynamics 12, Vol. 383, 1978.
  12. Klebanov, P., Tidstrom, K., and Sargent, L., The three dimensional nature of boundary layer instability, J. Fluid Mech., Vol. 12, 1962.
  13. Liu, C. and Liu, Z., Multigrid mapping and box relaxation for simulation of the whole process of flow transition in 3-D boundary layers, J. of Computational Physics, Vol. 119, pages 325--341, 1995.
  14. Lele, S. K., Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, Vol. 103, pages 16--42, 1992.
  15. Poinsot, T. J., Lele, S. K., Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys., Vol. 101, pages 104--129, 1992.
  16. Spekreijse, S. P., Elliptic grid generation based on Laplace equations and algebraic transformation, J. Comp. Phys., Vol. 118, pages 38--61, 1995.
  17. Thompson, K. W., Time dependent boundary conditions for hyperbolic systems, I, J. Comput. Phys., Vol. 68, pages 1--24, 1987.
  18. Thompson, K. W., Time dependent boundary conditions for hyperbolic systems, I, J. Comput. Phys., Vol. 89, pages 439--461, 1990.
  19. Visbal, M. R. and Gaitonde, D. V., High-order accurate methods for unsteady vortical flows on curvilinear meshes, AIAA Paper 98--013, 1998.
  20. Visbal, M. and Gaitonde, D., On the use of higher-order finite-difference schemes on curvilinear and deforming mashes, J. Comp. Physics, Vol. 181, pages 155--158, 2002.
  21. Yoon, S., Kwak D., Implicit Navier--Stokes solver for three-dimensional compressible flows, AIAA Journal, Vol. 30, pages 2653--2659, 1992.
Copyright Austral. Mathematical Soc.; prepared March 31, 2006, from Liu2.tex with anziamje.sty (v2.3k)