Numerical Simulation of Two–Dimensional Flow Past a Dimpled Cylinder Using a Pseudospectral Method

A numerical simulation of steady and unsteady two-dimensional flows past cylinder with dimples based on highly accurate pseudospectral method is the subject of the present paper. The vorticity and streamfunction formulation of two-dimensional incompressible NavierStokes equations with no-slip boundary conditions is used. The system is formulated on a unit disk using curvilinear body fitted coordinate system. Key issues of the curvilinear coordinate transformation are discussed, to show its importance in properly defined node distribution. For the space discretization of the governing system the Fourier-Chebyshev pseudospectral approximation on a unit disk is implemented. For steady flow simulations the non-linear time-independent Navier-Stokes problem is solved using the Newton’s method. For the time-dependent problem the semi-implicit third order Adams-Bashforth backward differentiation scheme is used. Finally numerical result for both steady and unsteady problems are presented. A comparison of results for the smooth cylinder with those from other authors shows good agreement. Spectral accuracy is demonstrated using the steady solver. Mathematics Subject Classification: 65M70, 35Q30, 76D17 1650 M. Kotovshchikova and S. H. Lui