Solution of the time-dependent Navier-Stokes equations for the flow around a circular cylinder

Traditionally, aerodynamicists, in order to simplify the theoretical treatment of determining the flowfield around an object, have developed special methods for treating the various viscous and relatively inviscid zones of the flow, including the shock wave, the shock layer, the boundary layer, and the wake. Thus the total flowfield has generally been obtained by patchwork. Although the foregoing approach certainly yields useful information, it is desirable to develop a method of solving the complete Navier-Stokes equations in which no such arbitrary assumptions are made. In the present paper, the authors present numerical solutions to the complete time-dependent Navier-Stokes equations for the transient supersonic flow around a right circular cylinder. The nonlinear partial differential equations for the conservation of mass, momentum, and energy were first expressed in cylindrical coordinates and then put into finite-difference form, making use of a new explicit-implicit, finitedifference scheme. These were analyzed for stability and convergence, and specific criteria were established for determining step sizes. Finally, numerical solutions were obtained for several Reynolds numbers for a freestream velocity of 10,000 fps.