Aerodynamic computations for a transonic projectile at angle of attack by total variation diminishing schemes

Several total variation diminishing (TVD) schemes and the Beam-Warming solution algorithm have been incorporated in a computer code for solving three-dimensional time-dependent, Reynold's averaged Navier-Stokes equations in generalized coordinates. A finite-volume fully implicit, approximately factored scheme is employed with a time-step convergence acceleration. Transonic turbulent flows past a scant ogive cylinder boat tail projectile at Mach numbers 0.94 and 0.97 including base flow region were studied. Conditions at 0- and 4-deg angle of attack were computed. Results of zero angle of attack showed that third-order TVD schemes gave little improvements over the second-order TVD schemes. Van Leer's third-order MUSCL-type TVD scheme yields somewhat better results and faster convergence than Chakravarthy's upwind-biased TVD scheme. The convergence rate of the Beam-Warming scheme is similar to that of the second-order TVD schemes. The Beam-Warming scheme gives comparative results over most of the projectile except regions of coarse grids because the scheme is very sensitive to grid resolution. For angle-of-attack computations, Van Leer's third-order MUSCL-type TVD scheme still gives better agreement with measurement.