A variation on MacCormack's method for axisymmetric viscous compressible flows

The use of the axisymmetric approximation in fluid-dynamics computations can provide considerable computational economy and greater resolution. However, it the flowfield in the vicinity of the axis is to be calculated, great care must be taken in choosing a finite difference scheme which properly models the axisymmetric form of the governing equations. The present investigation has the objective to present a suitable finite difference scheme which maintains all the desirable characeristics of an explicit technique reported by MacCormack (1969). The considered method has been successfully incorporated in computer codes which solve the Navier-Stokes and Euler equations by both relaxation and spatial marching techniques. It has also been used in a rocket engine nozzle/plume code.