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

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.