On the Discretization of the Continuous Adjoint to the Euler Equations in Aerodynamic Shape Optimization

                                
==Abstract==

In aerodynamic shape optimization, gradient-based algorithms usually rely
on the adjoint method to compute gradients. Working with continuous adjoint offers a
clear insight into the adjoint equations and their boundary conditions, but discretization
schemes significantly affect the accuracy of gradients. On the other hand, discrete ad joint computes sensitivities consistent with the discretized flow equations, with a higher
memory footprint though. This work bridges the gap between the two adjoint variants
by proposing consistent discretization schemes (inspired by discrete adjoint) for the con tinuous adjoint PDEs and their boundary conditions, with a clear physical meaning. The
capabilities of the new Think-Discrete-Do-Continuous adjoint are demonstrated, for in viscid flows of compressible fluids, in shape optimization in external aerodynamics.

== Full Paper ==
<pdf>Media:Draft_Sanchez Pinedo_69277504327_file.pdf</pdf>