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

• Published in: Journal of mechanical science and technology Vol. 33; no. 4; pp. 1731 - 1741
• Main Authors: Smith, B., Laoulache, R., Heryudono, A. R. H., Lee, J.
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Mechanical Engineers 01.04.2019; Springer Nature B.V; 대한기계학회
• Subjects: Aerodynamic coefficients; Approximation; Boundary conditions; Chebyshev approximation; Circular cylinders; Collocation methods; Computational fluid dynamics; Control; Dirichlet problem; Dynamical Systems; Engineering; Fluid flow; Industrial and Production Engineering; Laminar flow; Mechanical Engineering; Method of lines; Numerical methods; Partial differential equations; Reynolds number; Spectral methods; Strouhal number; Vibration; Vorticity; 기계공학; Flow over cylinder; Multiple boundary conditions; Navier-Stokes problem; Rectangular spectral collocation; Time stepping
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-019-0325-y

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.