| The motivation for this work arose from initial efforts in magnetohydrodynamics (MHD) flow control when plasma generated at high Mach numbers allows for electromagnetic actuators to change the characteristics of the flow. In the context of gradient-based optimization, this dissertation focuses on the problem of efficiently estimating the sensitivity of a given function of interest with respect to a large number of variables, in environments modeled by complex equations.; The discrete adjoint approach emerges as the best suitable option to deal with such complex equations and, in addition, allows for the use of automatic differentiation (AD) tools in the derivation of the adjoint solver. The selective application of AD is the central idea behind the Automatic Differentiation adjoint (ADjoint) approach. This approach has the advantages that it is applicable to arbitrary sets of governing equations and cost functions, and it is exactly consistent with the gradients that would be computed by exact numerical differentiation of the original solver. Furthermore, the approach is largely automatic, thus avoiding the lengthy development times usually required to develop discrete adjoint solvers for partial differential equations. It takes days, not years, to construct the ADjoint solver.; Sensitivities of aerodynamic coefficients with respect to several types of parameters, totaling over a half million variables, are computed and successfully validated against finite-difference approximations. The overall performance and accuracy of the method is shown to be better than conventional continuous adjoint approaches. The increased memory requirements can be eliminated at the expense of larger computational times for the ADjoint, that would bring the computational performance roughly on par with that of the best continuous adjoint solvers. |
