Comparison of Parabolized Vorticity and Navier-Stokes Solutions in a Mildly Nonorthogonal Coordinate System.

摘要

Two-dimensional, steady, incompressible, laminar flow in a diffuser and nozzle is considered as a model problem. A sheared mapping is used to provide a rectangular, wall-fitted, computational domain. This transformation produces a mildly nonorthogonal coordinate system in which the Navier-Stokes equations and parabolized vorticity approximation are solved. The discretization uses fourth-order accurate polynomial splines to resolve the wall boundary layer with a relatively sparse grid and standard finite differences in the main stream direction. The spline-finite difference equations are solved by line relaxation and Newton-Raphson iteration. Comparison of Navier-Stokes and parabolized vorticity results are presented for two diffusers (both with separation and reattachment of the boundary layer) and one nozzle flow. The parabolized and Navier-Stokes solutions are found to be in excellent agreement. Comparisons with a published parabolized result are also given. (Author)