Navier-Stokes computations past a prolate spheroid at incidence. I - Low incidence case

An analytical technique is developed based on the fully elliptic mode for calculating incompressible 3D viscous flows about a prolate spheroid at incidence. A system of numerically generated curvilinear coordinates is employed with Cartesian velocity components which act as dependent variables. A pressure solver couples the velocity and pressure fields by means of the PISO procedure by Issa (1985) in the context of a nonstaggered grid. Attention is given to the computational effort required per grid point in the formulation of the pressure solver based on an LU-preconditioned conjugate-gradient method. The main features of the vortical flows are effectively evaluated using the technique, and a pressure field is noted that results from the viscous-inviscid interaction. This predicted feature is supported by experimental evidence, and the velocity profiles and shear stresses are also shown to be accurate.