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Multigrid upwind Euler/Navier-Stokes computation on adaptive unstructured meshes

Published online by Cambridge University Press:  04 July 2016

Y. Zheng  and
L. He
Y. Zheng
Affiliation:
School of Engineering, University of Durham, UK
L. He
Affiliation:
School of Engineering, University of Durham, UK
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Abstract

An unstructured flow solver with adaptive mesh refinement and multigrid acceleration is developed to efficiently compute two-dimensional inviscid and viscous steady flows about complex configurations. High resolution is achieved by using the upwind scheme coupled with adaptive mesh refinement. An aspect-ratio adaptive multigrid method is developed and applied to effectively accelerate the solution convergence of the explicit time-marching in the near wall regions with high aspect mesh ratios. Numerical examples are presented for configurations and conditions ranging from transonic to low speed flows to demonstrate accuracy, speed, and robustness of the method.

Type
Research Article
Information
The Aeronautical Journal , Volume 105 , Issue 1046 , April 2001 , pp. 173 - 184
Copyright
Copyright © Royal Aeronautical Society 2001 

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References

1. Abhari, R.S. and Giles, M. A Navier-Stokes analysis of aerofoils in oscillating transonic cascades for the prediction of aerodynamic damping, ASME J Turbomachinery, January 1997,119.Google Scholar
2. Giles, M. and Haimes, R. Validation of a numerical method for unsteady flow calculations, ASME J Turbomachinery, January 1993, 115.Google Scholar
3. Dawes, W.N. The extension of a solution adaptive three-dimensional Navier-Stokes solver toward arbitrary complexity. ASME J Turboma chinery, April 1993, 115.Google Scholar
4. Dawes, W.N. The solution adaptive numerical simulation of the three-dimensional viscous flows in the serpentine coolant passage of a radial in flow turbine blade. ASME J Turbomachinery, January 1994, 116.Google Scholar
5. Frink, N.T. Recent progress toward a three-dimensional unstructured Navier-Stokes flow solver. 1994, AIAA paper 94-0061.Google Scholar
6. Marvriplis, D.J. Accurate multigrid solution of Euler equations on unstructured and adaptive meshes. AIAA J, 1990, 28, (2), pp 213–221.Google Scholar
7. Hawken, D.F. Review of some adaptive node-move techniques in finite element and finite difference solutions of partial differential equations. J Comp Phys, 1991, 95, pp 254–302.Google Scholar
8. Marvriplis, D.J. and Jameson, A. Multigrid solution of Euler equations on unstructured and adaptive meshes, 1987, ICASE 87-53.Google Scholar
9. Vilsmeier, R. and Hanel, D. Adaptive methods on unstructured grids for Euler and Navier-Stokes equations, computers fluids. Computers & Fluids, 1993, 22, (4/5), pp 483–499.Google Scholar
10. Pelletier, D. and Ilinca, F. Adaptive remeshing for the k-e model of turbulence. AIAA J, 1997, 35, (4).Google Scholar
11. Holmes, D.G. Unstructured grids and mesh adaptivity for inviscid and viscous flows, 1994, VKI lecture series.Google Scholar
12. Roehl, C. and Simon, H. Numerical simulation of compressible flows with adaptive unstructured grids, Proceedings of the third ASME/JSME joint fluids engineering conference, 1999, San Francisco, California, USA.Google Scholar
13. Sidén, G.L.D., Dawes, W.N. and Albråten, P.J. Numerical simulation of two-dimensional viscous compressible flow in blade cascades using a solution-adaptive unstructured mesh, ASME J Turbomachinery, 1990, 112.Google Scholar
14. Marvriplis, D.J. Three-dimensional multigrid for Euler equations. AIAAJ, 1992, 30, (2), pp 1,753-1,761.Google Scholar
15. Lallemand, M-H., Steve, H. and Dervieux, A. Unstructured multigridding by volume agglomeration: current status, Computers & Fluids, 1992,21,(3).Google Scholar
16. Connell, S.D. and Holmes, D.G. A 3D unstructured adaptive multigrid scheme for the Euler equations, AIAA J, 1994, 32, (2).Google Scholar
17. Sparlart, P.R. and Allmaras, S.R. A one-equation turbulence model for aerodynamic flows, 1992, AIAA paper 92-439.Google Scholar
18. Mitchel, C.R. Improved reconstruction schemes for the Navier-Stokes equations on unstructured meshes, January 1994, AIAA paper 91-1,106.Google Scholar
19. Frink, N.T. Assessment of an unstructured-grid method for predicting 3-D turbulent flows, 1996, AIAA paper, pp 96-292.Google Scholar
20. Roe, P.L. Approximate Riemann, parameter vectors and difference schemes, J Comp Phys, 1981, 43, pp 357–372.Google Scholar
21. Jameson, A., Schmidt, W. and Turkel, E. Numerical solutions of Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, 1981, AIAA paper 8l-1259.Google Scholar
22. Hirsch, C. Numerical Computation of Internal and External Flows. Vol 2, 1990, John Wiley & Sons, UK.Google Scholar
23. Wang, Q., et al Solving Navier-Stokes equations with advanced turbulence models on three-dimensional unstructured grids, 1999, AIAA paper, pp 99-156.Google Scholar
24. Pirzadeh, S. Structured background grids for generation of unstructured grids by advancing-front method, AIAA J, 1993, 31, (2), pp 257–265.Google Scholar
25. Warren, G.P., et al. Grid convergence for adaptive methods, 1991, AIAA paper 91-1,592.Google Scholar
26. Denton, J.D. An improved time-marching method for turbomachinery flow calculations. ASME J Eng for Gas Turbines and Power, 1983, 105, pp 514–524.Google Scholar
27. He, L. New two-grid acceleration method for unsteady Navier-Stokes calculations, J Propulsion and Power, 1993, 9, (2), pp 272–280.Google Scholar
28. He, L. Unsteady flow in oscillating turbine cascades: part 2 - computational study. ASME J Turbomachinery, April 1998, 120, pp 269–275.Google Scholar
29. Anderson, W.K., Thomas, J.L. and Leer, B.V. Comparison of finite volume flux vector splittings for the Euler equations, AIAA J, 1986, 24, (9),pp 1,453-1,460.Google Scholar
30. Cook, P., McDonald, M. and Firmin, M. Aerofoil RAE 2822 - pressure distributions and boundary layer wake measurement, 1979, AGARDAR-138.Google Scholar
31. He, L. Unsteady flow in oscillating turbine cascades: part 1 - linear cascade experiment, ASME J Turbomachinery, April 1998, 120, pp 262–268.Google Scholar