SENSITIVITY DERIVATIVES FOR ADVANCED CFD ALGORITHM AND VISCOUS MODELING PARAMETERS VIA AUTOMATIC DIFFERENTIATION

The computational technique of automatic differentiation (AD) is appli ed to a complicated computer program to illustrate the simplicity, eff iciency, and versatility of AD with complex algorithms for use within a sensitivity analysis. Many algorithmic and physics modeling coeffici ents appear in computer programs that are routinely set in an ad hoc m anner; AD can be used to enhance computer programs with derivative inf ormation suitable for guiding formal sensitivity analyses, which allow s these coefficient values to be chosen in a rigorous manner to achiev e particular program properties such as an improved convergence rate o r improved accuracy. In this paper, AD is applied to a three-dimension al thin-layer Navier-Stokes multigrid flow solver to assess the feasib ility and computational impact of obtaining exact sensitivity derivati ves with respect to algorithmic and physics modeling parameters typica l of those needed for sensitivity analyses. Calculations are performed for an ONERA Ms wing in transonic flow with both the Baldwin-Lomax an d Johnson-King turbulence models. The wing lift, drag, and pitching mo ment coefficients are differentiated with respect to two different gro ups of input parameters. The first group consists of the second- and f ourth-order damping coefficients of the computational algorithm, where as the second group consists of two parameters in the viscous turbulen t flow physics modeling. Results obtained via AD are compared for both accuracy and computational efficiency with the results obtained with divided differences (DD). The AD results are accurate, extremely simpl e to obtain, and show significant computational advantage over those o btained by DD for some cases.