The problem of supersonic flow control using fillets and sweep for a wing-body junction has been investigated numerically using a three-dimensional Navier-Stokes code, which employs the MacCormack's time-split finite volume technique. An elliptic grid generation technique with direct control over spacing has been developed for constructing the grid at a filleted wing-body junction. The computed results for pressure distribution, particle paths, and limiting streamlines on the flat plate and fin surface for a swept fin show a decrease in the peak pressure on the fin leading edge and in the extent of the separated flow region. Moreover, the results for filleted juncture clearly show that the flow streamline patterns lose much of their vortical character with proper filleting. It has been demonstrated that fillets with a radius of three-and-one-half times the fin leading-edge diameter are required to weaken the vorticity in the horseshoe vortex by a factor of three for the Mach number and Reynolds number considered in the present study. Nomenclature a -speed of sound CFL = Courant-Friedrichs-Lewy number Cf = skin friction coefficient D = diameter of the fin E = total energy per unit mass £/ = specific internal energy, T/y(y -1) H = height of the fin / = index in % direction j = index in 17 direction k -index in f direction L£, L^ L{ = finite difference operators in £, 17, and f directions M = Mach number Pri -laminar Prandtl number Pr t -turbulent Prandtl number p = static pressure R = radius of the fillet at the juncture T = static temperature t = time q = vector of conserved variables u -velocity component in x direction v = velocity component in y direction w = velocity component in z direction x, y, z = global coordinates X Q = distance from the flat plate leading edge to fin leading edge y = ratio of specific heats, c p /c v At = time step used in the split operators d = boundary-layer thickness A = fin sweep angle X = second coefficient of viscosity, -%/* jLt = dynamic molecular viscosity £, y, f = body oriented coordinates p = density a = safety factor in the stability criteria equation w = vorticity magnitude Subscripts t2