Sensitivity Derivatives for Advanced CFD Algorithm and Viscous Modeling Parameters via Automatic Differentiation

Abstract

The computational technique of automatic differentiation (AD) is applied to a complicated computer program to illustrate the simplicity, efficiency, and versatility of AD with complex algorithms for use within a sensitivity analysis. Many algorithmic and physics modeling coefficients appear in computer programs that are routinely set in an ad hoc manner; AD can be used to enhance computer programs with derivative information suitable for guiding formal sensitivity analyses, which allows these coefficient values to be chosen in a rigorous manner to achieve particular program properties such as an improved convergence rate or improved accuracy. In this paper, AD is applied to a three-dimensional thin-layer Navier–Stokes multigrid flow solver to assess the feasibility and computational impact of obtaining exact sensitivity derivatives with respect to algorithmic and physics modeling parameters typical of those needed for sensitivity analyses. Calculations are performed for an ONERA M6 wing in transonic flow with both the Baldwin–Lomax and Johnson–King turbulence models. The wing lift, drag, and pitching moment coefficients are differentiated with respect to two different groups of input parameters. The first group consists of the second- and fourth-order damping coefficients of the computational algorithm, whereas the second group consists of two parameters in the viscous turbulent 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 simple to obtain, and show significant computational advantage over those obtained by DD for some cases.