A transformation-free HOC scheme for incompressible viscous flows on nonuniform polar grids
We recently proposed a transformation-free higher-order compact (HOC) scheme for two-dimensional (2-D) steady convection-diffusion equations on nonuniform Cartesian grids (It. J. Numer Meth. Fluids 2004; 44:33-53). As the scheme was equipped to handle only constant coefficients for the second-order derivatives, it could not be extended directly to curvilinear coordinates, where they invariably occur as variables. In this paper, we extend the scheme to cylindrical polar coordinates for the 2-D convection-diffusion equations and more specifically to the 2-D incompressible viscous flows governed by the Navier-Stokes (N-S) equations. We first apply the formulation to a problem having analytical Solution and demonstrate its fourth-order spatial accuracy. We then apply it to the flow past ail impulsively started circular cylinder problem and finally to the driven polar cavity problem. We present our numerical results and compare them with established numerical and analytical and experimental results whenever available. This new approach is seen to produce excellent comparison in all the cases. Copyright (C) 2009 John Wiley & Sons, Ltd.
nonuniform circular cylinder polar cavity hoc convection-diffusion n-s equations