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AUTOMATIC
DIFFERENTIATION OF
ADVANCED CFD CODES FOR MULTIDISCIPLINARY DESIGN

C. Bischof1 and G. Corliss 2

Argonne National Laboratory, Argonne, Illinois

L. Green
NASA Langley Research Center, Hampton, Virginia

A. Griewank1

Argonne National Laboratory, Argonne, Illinois

K. Haigler and P. Newman
NASA Langley Research Center, Hampton, Virginia

Argonne Preprint MCS-P339-1192

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown here that sensitivity derivatives can be obtained accurately and efficiently by using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier{Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that, using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3{D CFD code in a relatively short time, e.g. O(manweek) not O(man-year).

1This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U. S. Department of Energy, under Contract W-31-109-Eng-38.
2This work was supported by the National Science Foundation under Cooperative Agreement Number CCR-9120008.

1 Nomenclature

CD Wing drag coefficient
CL Wing lift coefficient
CM Wing pitching moment coefficient D Generic sensitivity derivative
I Identity matrix
J Jacobian matrix
M Free stream Mach number
P Preconditioner matrix
R Residual vector for flow equations
Re Reynold's number (mean chord)
S Seed matrix
x Design variable
y Discrete mesh coordinates
z Local flow (state) variable
Angle-of-attack
ae Spectral radius
Subscripts
AD Automatic differentiation
DD Divided difference
m Iteration index
x Partial derivative w.r.t. x
y Partial derivative w.r.t. y
z Partial derivative w.r.t. z
? Root of R = or iteration-fixed-point
Superscripts
(prime) Total derivative w.r.t. x
~ (tilde) Approximate operator

2 Introduction

In the past, design of flight vehicles typically required the interaction of many technical disciplines over an extended period of time in a more or less sequential manner. At present, computer-automated discipline analyses and interactions offer the possibility of significantly shortening the design-cycle time, while simultaneous multidisciplinary design optimization (MDO) via formal sensitivity analysis (SA) holds the possibility of improved designs. Recent topical conferences 3 [1{8], [10, 12, 34, 35, 54, 55] for example, attest to the interest in these possibilities for improving aerospace vehicle design processes and procedures. Advances in computer hardware and software, electronic communications, and discipline solution algorithms and codes will individually contribute; however, true synergisms may be required to make it all feasible. This paper addresses one such synergism for computa-

3Those without published proceedings include the 1992 AIAA/AHS/ASEE Aerospace Design Conference, Feb. 1992, and the AIAA Aircraft Design Systems Meeting, Aug. 1992.