Discrete mesh coordinates : Local flow (state) variable a Angle-of-attack p Spectral radius Subscripts .4D Automatic differentiation Automated muhidisciplinary design of aircraft and DD Divided difference other flight vehicles requirc_ the optimization of complex performance objectives with respect to a number of design m Iteration index parameters and constraints. The effect of these indepen-z Partial derivative w.r.t, z dent design variables on the system performance criteria Y Partial derivative w.r.t, y can be quantified in terms of sensitivity derivatives which : Partial derivative w.r.t. : * Root of R = 0 or i_eration-fixed-point must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis Superscripts ' (prime) Total derivative w.r.t, z codes do not provide such derivatives as part of a flow soiutioa; these derivatives are very expeasive to obtain by (tihh:) ApprGximate operator divided (finite) differences from perturbed solutions, lt is shown here that se,sitivity derivatives can be obtained 2

Sensitivity derivative (SD) calculation via automatic differentiation (AD) typical of that required for the aerodynamic design of a transport-type aircraft is considered. Two ways of computing SD via code generated by the ADIFOR automatic differentiation tool are compared for efficiency and applicability to problems involving large numbers of design variables.A vector implementation on a Cray Y-MP computer is compared with a coarse-grained parallel implementation on an IBM SP1 computer, employing a Fortran M wrapper.The SD are computed for a swept transport wing in turbulent, transonic flow; the number of geometric design variables varies from 1 to 60 with coupling between a wing grid generation program and a state-of-the-art, 3-D computational fluid dynamics program, both augmented for derivative computation via AD. For a small number of design variables, the Cray Y-MP implementation is much faster.As the number of design variables grows, however, the IBM SP1 becomes an attractive alternative in terms of compute speed, job turnaround time, and total memory available for solutions with large numbers of design variables. The coarse-grained parallel implementa-

Conservative Fu II-Poten t ial Calculations for Axisymmetric, Transonic FlowAbstract A conservative, finite-difference, fullpotential relaxation code has been developed to solve transonic flow around axisymmetric or nonlifting, planar, two-dimensional bodies. The program utilizes the artificial compressibility method to provide an upwind bias in supersonic regions. calculated examples include a wide variety of axisymmetric and planar two-dimensional shapes with various blunt, pointed and open ends in subsonic, transonic, and low supersonic free streams. Comparisons between conservative and nonconservative full-potential calculations show perfect agreement at convergence when the flow is entirely subsonic. Noticeable differences exist, however, between the conservative and nonconservative solutions for transonic flows with shocks.