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In this paper, a global method of generalized differential quadrature (GDQ) is applied to solve the two-dimensional incompressible Navier-Stokes equations in the curvilinear coordinate system. The vorticity-stream function formulation was used. Numerical results for a smooth expansion channel flow demonstrated that accurate numerical results can be obtained using a considerably small number of grid points.

In the present work, the Osher-Chakravarthy's upwind scheme with Roe's Riemann solver is applied to solve the three-dimensional, turbulent, parabolized Navier-Stokes (PNS) equations. The governing equations are discretized by a finite volume approach, and the turbulence closure for the Reynolds stress is obtained by using a algebraic turbulence model of Baldwin-Lomax. The present PNS solver can be used for marching the solution downstream from a given initial data surface and also for generating the starting solution. Along each plane in the marching direction, the resultant algebraic equation system was solved by Strongly Implicit Procedure (SIP). Application of present solver to a test problem showed that the present numerical results agree well with the experimental data and other numerical results.