1. The governing equations IEqs. 1-15) were solved numerically using the explicit, finitedifference scheme of MacCormack (ref. 12). The method consists of predictor and corrector steps resulting i n second-order accuracy both spatially and temporally. The numerical stability of the scheme was mintained by the Courant-Friedrichs-Lewy (CFL) rule. Global time steps were used to ensure time-accura te so 1utions. The Fortran-200 coding of the algorithm for COC Cyber-205 computer was based on the inlet-code of ref. 13.
2. Aboundary layer profile was generated by running the code in two-dimensions (X-Y) prior to the three-dimensional computations, and it was imposed a t the upstream boundary. Experimentally determined values of the boundary layer thickness and the momentum thickness a t the front lio of d the cavity were mtched exactly. No-slip, impermeabilitv, adiabatic and zero-normagradient of Pressure, conditions were imposed a t solid surfaces. First-order extrapolation for the conserved variables were used a t the downstream and lateral-outboard boundaries. The outer boundary conditions were specified after a flow direction check. When the sign of the contravariant velocity in ?direction (Eq. (11)) was negative (inflow), property values were set equal to their freestream values, and first-order extrapolation from the computation zone was applied otherwise (outflow). The symmetry of the flow at 2 - 0 plane was ensured by setting the 2- component of velocity equal to zero and applying first-order extrapolation for the other conserved variables at this plane. The velocity vectnrs for all the dummy points were set equal to zero. In order to eliminate the effects of dummy points, shear stress and heat flux terms for all grid points on and next to the walls were recomputed, using differences only towards the computation zone i n predictor and corrector steps. The boundary conditions were applied in both the predictor and corrector steps. The portion of the computational zone above the cavity was initialized with the boundary layer profile generated for the upstream. The initial values for points inside the cavity were set for a very slow streamwise flow.
3. This work was supported under NASA Grant NO. NAG-1-664.
4. "Supersonic Axial-Force Characteristics of a Rectangular-Box Cavity with Varioy Lengthto-Depth Ratios i n a Flat Plate, NASA-TM87659, December 1986.