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Numerical study of rectangular spectral collocation method on flow over a circular cylinder

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Abstract

Laminar flow over a circular cylinder has been widely used as a classical benchmark test for various numerical methods for partial differential equations. One of the popular ways is by using the vorticity-streamfunction formulation of the Navier-Stokes equations on a bounded numerical domain. The partial differential equations are solved numerically by the method of lines, where space is discretized using the standard collocation method, subject to multiple boundary conditions in the form of Dirichlet at the inlet and Neumann at the outlet. The resulting system of equations are then advanced in time using multistep methods. Fourier-Chebyshev pseudospectral method is used to approximate the solutions in space and Adams-Bashforth third-order backward differentiation method is employed as a time-stepping method. The rectangular spectral collocation method, developed by Driscoll and Hale, is applied to solve the ambiguity in imposing multiple boundary conditions on the same boundary points. The numerical simulations show very good agreement with similar studies for the Strouhal number, drag and lift coefficients over Reynolds numbers ranging from 50 to 150.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Massachusetts, Dartmouth, MA, 02747, USA

    B. Smith & R. Laoulache

  2. Department of Mathematics, University of Massachusetts, Dartmouth, MA, 02747, USA

    A. R. H. Heryudono & J. Lee

  3. Department of Mechanical and Design Engineering, Hongik University, Sejong, 30016, Korea

    J. Lee

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  1. B. Smith
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  2. R. Laoulache
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  3. A. R. H. Heryudono
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  4. J. Lee
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Correspondence to J. Lee.

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Recommended by Associate Editor Donghyun You

Benjamin Smith received his M.S. from University of Massachusetts, Dartmouth in 2015 and B.S. from Massachusetts Institute of Technology in 2005. He served US Army as a platoon leader and works as a research engineer for Aurora Flight Science Corporation. He is interested in numerical methods using both custom written and commercially available codes.

Raymond Laoulache received his Ph.D. from Brown University in 1987, M.S. and B.S. from Northeastern University in 1983 and 1980, respectively, and joined Dept. of Mechanical Engineering of University of Massachusetts, Dartmouth in 1988. His research interests are in computational fluid dynamics & renewable energy. His research is in the area of modeling hydrokinetic crossflow turbines. He is the author of Advanced Engineering Mathematics: Applications Guide, published by John Wiley & Sons, Inc.

Alfa R. H. Heryudono has been with Mathematics Dept, University of Massachusetts Dartmouth since 2008. He graduated from University of Delaware with Ph.D. in Applied Mathematics in 2008. He is interested in research in scientific computing and numerical methods for PDEs; radial basis function methods, pseudospectral methods, numerical conformal mapping, and tear film dynamics.

Jinhee Lee received B.S. and M.S. degrees from Seoul National University and KAIST in 1982 and 1984, respectively. He received his Ph.D. from University of Michigan, Ann Arbor in 1992 and joined Dept. of Mechanical and Design Engineering of Hongik University, Sejong, Korea. His research interests include inverse problems, pseudospectral method, vibration and computational fluid dynamics.

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Smith, B., Laoulache, R., Heryudono, A.R.H. et al. Numerical study of rectangular spectral collocation method on flow over a circular cylinder. J Mech Sci Technol 33, 1731–1741 (2019). https://doi.org/10.1007/s12206-019-0325-y

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  • DOI: https://doi.org/10.1007/s12206-019-0325-y

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