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The paper discusses results obtained with a finite-volume code that simulates viscous, turbulent flows for 3-D, adaptive, unstructured meshes. The implementation uses a cell-centered, face-based data structure. A fully explicit, second-order accurate, five-stage, Runge-Kutta time stepping scheme is used to perform the time marching of the flow equations. Spatial discretization of the Reynolds-averaged Navier-Stokes equations can be performed with second-order centered or upwind schemes. Automatic grid refinement routines are considered to adapt the original mesh. A sensor based on density gradients selects the volumes to be refined. The code is able to handle tetrahedra, hexahedra, wedges, and pyramids. A full multigrid scheme is available to accelerate convergence to steady state. Coarse grid levels are constructed through an agglomeration procedure. One-and two-equation turbulence models are implemented to include the turbulent effects into the numerical formulation. The mentioned features integrated in one single code allow the Brazilian aerospace program to simulate complex flow conditions for sounding rockets and satellite launch vehicles with accuracy and reasonable computational resources. Good agreement with theoretical or experimental results is obtained with the present numerical tool. Nomenclature a = speed of sound C = convective operator Cp = pressure coefficient D = artificial dissipation operator d = minimum distance to the wall e = total energy per unit volume e i = internal energy f = source term of the multigrid method k = specific turbulent kinetic energy p = static pressure P e = inviscid flux vector P v = viscous flux vector Q = vector of conserved properties q = heat flux vector RHS = right-hand side operator S = absolute value of the mean strain-rate tensor S = area vector S ij = mean strain-rate tensor component T = static temperature u, v, w = Cartesian velocity components V = viscous operator v = Cartesian velocity vector x, y, z = Cartesian coordinates = angle of attack 1 . . . 5 = Runge-Kutta control parameters = ratio of specific heats t = time step = von Karman constant = dynamic viscosity coefficient = kinematic viscosity coefficient = modified Spalart-Allmaras eddy-viscosity coefficient = density = viscous stress tensor = gradient ratio for limiter computation = control volume limiter ! = turbulent dissipation = absolute value of the mean rotation tensor ij = mean rotation tensor component Subscripts f, k = face index i, m = grid control volume indices ' = laminar property L, R = interface left and right properties t = turbulent property 1 = freestream property Superscripts (m) = current grid of the multigrid method n = time instant * = dimensional property

Transonic and supersonic flow simulations over typical launch vehicle configurations are presented. A 3-D finite difference numerical code, written for general, curvilinear, body-conforming coordinate systems, is used. The code solves the thin-layer approximation for the laminar Navier-Stokes equations. Simulations are performed for a launcher and a sounding rocket configurations, currently under development at Instituto de Aeronáutica e Espaço. Calculations consider cases at angle of attack and at various freestream Mach numbers. Normal force coefficients are obtained such that the loads required for the design phase can be determined. Computational results are compared to available experimental data. In general, good results within engineering error margins are obtained

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