Automatic differentiation of advanced CFD codes for multidisciplinary design

Abstract

Automated multidisciplinary design of aircraft and other ight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The eect of these indepen-dent design variables on the system performance criteria can be quantied in terms of sensitivity derivatives which must be calculated and propagated by the individual dis-cipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a \now so-lution; these derivatives are very expensive to obtain by divided ( nite) dierences from perturbed solutions. It is shown here that sensitivity derivatives can be obtained accurately and eciently by using the ADIFOR source translator for automatic dierentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier{Stokes, multigrid ow solver called TLNS3D is amenable to au-tomatic dierentiation in the forward mode even with its implicit iterative solution algorithm and complex turbu-lence modeling. It is signicant that, using computational dierentiation, consistent discrete nongeometric sensitiv-ity derivatives have been obtained from an aerodynamic 3{D CFD code in a relatively short time, e.g. O(man-week) not O(man-year). 1 This work was supported by the AppliedMathematical Sciences