Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes

A comprehensive strategy for developing and implementing discrete adjoint methods for aerodynamic shape optimization problems is presented. By linearizing each procedure in the entire optimization problem, transposing each linearization, and reversing the sequential order of operations, the adjoint of the complete optimization problem, including flow equations and mesh motion equations is constructed in a modular and verifiable fashion. This construction is also shown to produce minimal memory overheads, and retain the same convergence characteristics of the original analysis problem in the sensitivity analysis. These techniques are implemented in a three-dimensional unstructured multigrid NavierStokes solver, and demonstrated on a transonic drag reduction problem for a wing body configuration.