Theory and Implementation of Shape Sensitivities in a Rapid Hypersonic Impact Method (HI-Mach)

This paper describes a method for obtaining sensitivities of a quantity of interest with respect to the geometry in a hypersonic panel code. The hypersonic panel code (HI-Mach) implements impact methods to approximate quantities such as lift, drag, wall temperature, and heat flux. Because many of the methods within the hypersonic impact method are simple, direct analytical derivatives of these methods are obtained and presented. In the few cases where the analytic approach involves exceptionally complex derivatives, approximate techniques are described. The derivative calculations were verified against finite-difference results and showed near machine-precision agreement. The computational complexity is O(