Numerical simulation of 2D flow past a dimpled cylinder using a pseudospectral method

Abstract

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 thesis. The vorticity-streamfunction formulation of two-dimensional incompressible Navier-Stokes 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. To handle the singularity at the pole of the unit disk the approach of defining the computational grid proposed by Fornberg was implemented. Two algorithms for solving steady and unsteady problems are presented. 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. In both algorithms the fully coupled system with two no-slip boundary conditions is solved. Finally numerical result for both steady and unsteady solvers 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.