Commun. Comput. Phys., 12 (2012), pp. 1163-1182.


The Biharmonic Approach for Unsteady Flow Past an Impulsively Started Circular Cylinder

Jiten C Kalita 1*, Shuvam Sen 2

1 Department of Mathematics, Indian Institute of Technology Guwahati, PIN 781039, India.
2 Department of Mathematical Sciences, Tezpur University, PIN 784028, India.

Received 20 April 2011; Accepted (in revised version) 12 December 2011
Available online 17 April 2012
doi:10.4208/cicp.200411.121211a

Abstract

In this paper, a newly developed second order temporally and spatially accurate finite difference scheme for biharmonic semi linear equations has been employed in simulating the time evolution of viscous flows past an impulsively started circular cylinder for Reynolds number Re up to 9,500. The robustness of the scheme and the effectiveness of the formulation can be gauged by the fact that it very accurately captures complex flow structures such as the von Karman vortex street through streakline simulation and the $\alpha$ and $\beta$-phenomena in the range $3,000 \leq Re \leq 9,500$ among others. The main focus here is the application of the technique which enables the use of the discretized version of a single semi linear biharmonic equation in order to efficiently simulate different fluid structures associated with flows around a bluff body. We compare our results, both qualitatively and quantitatively, with established numerical and more so with experimental results. Excellent comparison is obtained in all the cases.

AMS subject classifications: 35Q30, 65M06, 76D05, 76D25

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Key words: Biharmonic, non-rectangular, N-S equations, transient, circular cylinder, von Karman vortex street.

*Corresponding author.
Email: jiten@iitg.ernet.in (J. C. Kalita), shuvam@tezu.ernet.in (S. Sen)
 

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