Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-19T00:07:57.400Z Has data issue: false hasContentIssue false
  • English
  • Français

Simulation of Flow Past a Cylinder With Adaptive Spectral Element Method

Published online by Cambridge University Press:  09 September 2016

L.-C. Hsu ,
J.-Z. Ye  and
C.-H. Hsu
L.-C. Hsu*
Affiliation:
Department of Mechanical EngineeringNational Yunlin University of Science and TechnologyYunlin, Taiwan
J.-Z. Ye
Affiliation:
Department of Mechanical EngineeringNational Yunlin University of Science and TechnologyYunlin, Taiwan
C.-H. Hsu
Affiliation:
Department of Mechanical EngineeringNational Yunlin University of Science and TechnologyYunlin, Taiwan
*
*Corresponding author ([email protected])
Get access

Abstract

The simulations of flow past a two-dimensional circular cylinder are conducted to investigate the feasibility of adaptive mesh refinement applied on curved spectral elements. The nonconforming spectral element method and adaptive meshes technique are used to the curve surfaces and observe whether any discontinuity of the solutions. The adaptive nonconforming spectral element method is implemented to compare with those obtained by conforming mesh method with respect to several existing numerical and experimental studies. Meanwhile, three kinds of estimated error base mesh adaptation are conducted to compare their accuracy and efficiency with conforming mesh method. The results show adaptive nonconforming mesh method is more efficient than the conforming method. Especially, the vorticity error based method performs highest accuracy and fastest convergence. The results show this mesh refinement technique is applicable on the curved elements with satisfactory accuracy. It releases this technique may be applied on the simulations of flow past objects with more general geometries.

Keywords

Adaptive meshesVorticity basedSpectral elementCylinderVortex
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 235 - 247
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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. Patera, A. T., “A spectral element method for fluid dynamics: laminar flow in a channel expansion,” Journal of Computational Physics, 54, pp. 468–488 (1984).Google Scholar
2. Maday, Y., Mavriplis, C. and Patera, A.T., “Nonconforming mortar element methods: Application to spectral discretization,” Domain Decomposition Methods, Chan, T., Periaux, J., Widlund, O.B., Eds., SIAM, Philadelphia, pp. 392–418 (1989).Google Scholar
3. Bernardi, C., Maday, Y. and Patera, A.T., “A new nonconforming approach to domain decomposition: the mortar element method,” Non-linear Partial Differential Equations and their Applications, Brezis, H., Lions, J. L., Eds., Pitman/Wiley: Lon-don/New York, 11, pp.13–51 (1994).Google Scholar
4. Mavriplis, C. and Hsu, L.-C., “A two-dimensional adaptive spectral element method,” Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, Snowmass, USA (1997).Google Scholar
5. Feng, H. and Mavriplis, C., “Adaptive spectral element simulations of thin premixed flame sheet deformations,” Journal of Scientific Computing, 17, pp. 385–395 (2002).Google Scholar
6. Feng, H. and Mavriplis, C., Van der Wijngaart, R. and Biswas, R., “Parallel 3D mortar element method for adaptive nonconforming meshes,” Journal of Scientific Computing, 27, pp. 231–243 (2006).Google Scholar
7. Henderson, R. D. “Dynamic refinement algorithms for spectral element methods,” Computer Methods in Applied Mechanics and Engineering, 175, pp. 395–411 (1999).CrossRefGoogle Scholar
8. Premasuthan, S., Liang, C. and Jameson, A. “Computation of flows with shocks using the Spectral Difference method with artificial viscosity, II: Modified formulation with local mesh refinement,” Computers & Fluids, 98, pp. 122–133 (2014).Google Scholar
9. Kopera, M. A. and Giraldo, F. X. “Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations,” Journal of Computational Physics, 275, pp. 92–117 (2014).Google Scholar
10. Dupont, F. and Lin, C. “The adaptive spectral element method and comparisons with more traditional formulations for ocean modeling,” Journal of Atmosphere and Ocean Technology, 21, pp. 135–147 (2004).Google Scholar
11. Orszag, S.A. and Kells, L.C. “Transition to turbulence in plane poiseuille and plane couette flow,” Journal of Fluid Mechanics, 96, pp. 159–205 (1980).Google Scholar
12. Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, (1971).Google Scholar
13. Golub, G. H. and Van Loan, C. F., Matrix Computations, The Johns Hopkins University Press, Baltimore, (1985).Google Scholar
14. Mavriplis, C. “Nonconforming Discretizations and a Posteriori Error Estimators for Adaptive Spectral Element Techniques”, Ph. D. Dissertation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Massachusetts, U.S. (1989).Google Scholar
15. Oh, W.S., Kim, J.S. and Kwon, O.J. “Time-accurate Navier–Stokes simulation of vortex convection using an unstructured dynamic mesh procedure,” Computers & Fluids, 32, pp. 727–749 (2003).Google Scholar
16. Rausch, R.D., Batina, J.T. and Yang, H.T.Y., “Spatial adaptation of unstructured meshes for unsteady aerodynamic flow computations,” AIAA Journal, 30, pp. 1243–1251 (1992).Google Scholar
17. Hwang, C. J. and Kuo, J. Y. “Adaptive finite volume upwind approaches for aeroacoustic computations,” AIAA Journal, 35, pp. 1286–1293 (1997).Google Scholar
18. Park, J., Kwon, K. and Choi, H., “Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160,” KSME International Journal, 12, pp. 1200–1205 (1998).CrossRefGoogle Scholar
19. Apelt, C. “The Steady flow of viscous fluid past a circular cylinder at Reynolds number 40 to 44,” A.R.C. Technical Report, R & M. No. 3175, Aeronautical Research Council, Ministry Of Aviation, London (1961).Google Scholar
20. Posdziech, O. and Grundmann, R. “A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder,” Journal of Fluids and Structures, 23, pp. 479–499 (2007).Google Scholar
21. Hammache, M. and Gharib, M. “An experimental study of the parallel and oblique vortex shedding from circular cylinders,” Journal of Fluid Mechanics, 232, pp. 567–590 (1991).CrossRefGoogle Scholar
22. Williamson, C. H. K., “The existence of two stages in the transition to three dimensionality of a cylinder wake,” Physics of Fluids, 31, pp. 3165–3168 (1988).Google Scholar
23. Williamson, C. H. K. and Roshko, A., “Measurements of base pressure in the wake of a cylinder at low Reynolds numbers,” Zeitschrift Flugwissenschaften und Weltraumforschung, 14, pp. 38–46 (1990).Google Scholar
24. Henderson, R. D., “Details of the drag curve near the onset of vortex shedding,” Physics of Fluids, 7, pp. 2102–2104 (1995).Google Scholar
25. Rajani, B.N., Kandasamy, A. and Majumdar, S., “Numerical simulation of laminar flow past a circular cylinder,” Applied Mathematical Modeling, 33, pp. 1228–1247 (2009).Google Scholar
26. Roshko, A., “On the development of turbulent wakes from vortex streets,” NACA Report 1191 (1954).Google Scholar
27. Norberg, C., “An experimental investigation of the flow around a circular cylinder: influence of aspect ratio,” Journal of Fluid Mechanics, 258, pp. 287–316 (1994).CrossRefGoogle Scholar
28. Lange, C., “Numerical predictions of heat and momentum transfer from a cylinder in crossflow with implications to hot-wire anemometry”. Ph.D. Dissertation, Friedrich-Alexander University Erlangen-Nürnberg, Germany (1997).Google Scholar
29. Homann, F., “Influence of higher viscosity on flow around cylinder,” Forsch. Gebiete Ingenieur, 17, pp. 1–10 (1936).Google Scholar
30. Thom, A., “The flow past circular cylinder at low speeds,” Proeedingc Royal Society Series A, 141, pp. 651–669 (1933).Google Scholar
31. Persillon, A. and Braza, M., “Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation,” Journal of Fluid Mechanics, 365, pp. 23–88 (1998).Google Scholar
32. Norberg, C., “Pressure distributions around a circular cylinder in cross-flow,” Symposium on Bluff Body Wakes and Vortex-Induced Vibrations (BBVIV3), Hourigan, K., Leweke, T., Thompson, M.C., Williamson, C.H.K. Eds., Port Arthur, Queensland, Australia, Monash University, Melbourne, Australia, pp. 1–4 (2002).Google Scholar