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

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 adjoint 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 continuous adjoint PDEs and their boundary conditions, with a clear physical meaning. The capabilities of the new Think-Discrete-Do-Continuous adjoint are demonstrated, for inviscid flows of compressible fluids, in shape optimization in external aerodynamics.