Pseudospectral approximation in a three-dimensional Navier-Stokes code

A pseudospectral solution scheme is described for three-dimensional Navier-Stokes equations. The method, based on Fourier series, is employed for computing approximate derivatives in the circumferential direction and finite difference approximations in the other directions of a curvilinear coordinate system. The coordinate system is fitted to missile-shaped configurations at moderate angles of attack. A sample problem is worked out for the flow over a hemispherical cylinder in a freestream Mach 1.2 flow. The pseudospectral model is shown to be more accurate than a fourth order model, particularly in the forebody region, where the nose separation pattern and crossflow separation agreed with flow visualization data.