The Use of Dual Number Automatic Differentiation With Sensitivity Analysis to Investigate Physical Models

Abstract

Local sensitivities are explored using dualnumberautomaticdifferentiation (DNAD) across three mathematical models of physical systems that have increasing complexity. The models are: (1) a model for the approach of a sphere to free fall; (2) the Tayloranalogybreakup (TAB) model for liquid droplet atomization; and, (3) an evaluation of the BHR model of turbulence for the development of onedimensional Rayleigh–Taylor driven material mixing. Sensitivity and functional shape parameters are developed that permit a relative study to be quickly performed for each model. Furthermore, compensating errors, measurement parameter sensitivity, and feature sensitivities are investigated. The test problems consider transient (initial condition effects), steady state (final functional forms), and measures of functional shape. Reduced model forms are explored and selected according to sensitivity. Aside from the local sensitivity studies of the models and associated results, DNAD is shown to be one of several useful, quickly implemented tools to investigate a variety of sensitivity effects in models and together with the present results may serve as a means to simplify a model or focus future model developments and associated experiments.