Department of Aerospace Engineering, University of Glasgow
Abstract
A multi-domain generalized differential quadrature method for the solution of two-dimensional, steady, incompressible Navier-Stokes equations in the stream function-vorticity formulation around an arbitrary geometry is presented, and applied to the flows past a backward facing step and a square step in a channel. In each subdomain, the spatial derivatives are discretized by local generalized differential quadrature. The resultant set of ordinary differential equations for vorticity are solved by the 4-stage Runge-Kutta scheme, and the set of algebraic equations for the stream function are solved by LU decomposition. Patching conditions at the interface of subdomains are used. A residual averaging technique is applied to accelerate the convergence to steady state resolution. Good agreement is obtained, compared with available experimental data and other numerical results even though only a few grid points are used
