Time-Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow

An efficient numerical method for calculating plane, axisymmetric, and fully three-dimensional blunt-body flow is presented. It is a second-order-a ccurate, time-dependent finite-volume procedure that solves the Euler equations in integral conservation-law form. These equations are written with respect to a Cartesian coordinate system in which an embedded mesh adjusts in time to the motion of the bow shock that is automatically captured as part of the weak solution. With such an adjusting mesh, oscillations in flow properties near the shock are shown to be virtually eliminated. The scheme uses a time-splitting concept that accelerates the convergence appreciably. Comparisons are made between computed and experimental results. HE computation of the in viscid subsonic-transonic flowfield about a blunt body has been the focus of numerous numerical investigations during the past 10 to 15 years. Deter- mining the fluid properties of either real or perfect gases about the noses of supersonic and hypersonic airplanes and re-entry spacecraft provides the necessary data for the subsequent evalua- tion of the radiative and convective heat-transfer rates and boundary-layer effects on the aircraft body. It also serves to initiate the downstream calculation of the supersonic portion of the flowfield about such vehicles.1"5 Another application for these calculations is the study of transonic flow about blunt leading edges. The need and importance of determining all such flowfields have continued the interest in blunt-body methods, particularly those that will handle complicated three-dimensional geometries at high incidence angles. At the present time, three general classes of numerical methods are appropriate for the blunt-body problem :6 1) inverse method,7"9 2) method of integral relations,10"12 and 3) time- dependent finite-difference methods.13"32 The latter methods provide a means of treating the problem of inviscid supersonic flow past a blunt body as an initial-value problem since the equations for unsteady flow are always hyperbolic.J Results for steady flow are obtained as the limiting state reached asymp- totically in time by an unsteady flow with constant freestream conditions, a solid stationary body boundary, and suitably chosen initial conditions. This approach appears to be the most convenient for computing flow with either large asymmetry or extensive transonic regions as well as embedded discon- tinuities.14'15 For such cases this numerical technique has two important advantages: being equally suited for computing either subsonic or supersonic flow and being capable of approximating weak solutions of the Euler gasdynamic equations. The time-dependent methods that have been developed for inviscid compressible flow past blunt bodies traveling at super- sonic speeds may be classified according to their order of accuracy in terms of mesh spacing. Evans and Harlow16'17