Ole Burghardt

• In this thesis, we consider optimization problems with objective functions that, for their evaluation, require to solve large systems of equations. In computational fluid mechanics, such systems can, for example, arise from discretizations of the Euler or Navier-Stokes equations. When applying deterministic, gradient-based optimization algorithms, one needs to compute gradients of the objective function with respect to a high number of optimization parameters, too, which, for this reason, may lead to significant computational cost. Via the so-called discrete adjoint method, the entire gradient of the objective function can be derived from a single numerical solution to an adjoint equation, based on a linearized form of the system of equations, at a constant computational cost. For many problems in aero- and hydrodynamics, in structural mechanics or in finance, this approach has already become well-established. In the field of multi-disciplinary optimization (MDO), the linearization of coupled systems of equations, i.e. systems of equations that depend additionally on state variables of one or more other systems, yields to cross derivatives that result in a coupling of the adjoint equations and solvers. For the evaluation and the exchange of cross derivatives in a multi-disciplinary discrete adjoint solver, we propose a method that generalizes and automizes the procedure, with a focus on software for multiphysics problems. In this way, a multi-disciplinary discrete adjoint solver can adapt to multiple problem configurations, independent of the number and types of disciplines and couplings, without having to change or adjust its numerical implementation. This is achieved by employing algorithmic differentiation in reverse mode in combination with a specialized design of the computational graph, which we will demonstrate by means of an implementation in the open-source software SU2. Furthermore, such a computational graph allows to transfer the recursive projection method for stabilization and acceleration of iterative schemes, which has already been applied for conventional adjoint methods, to the multi-disciplinary context. For our implementation, we will show how it can be added as a set of non-intrusive correction routines. Finally, on the basis of a common cylinder flow configuration, we will test and validate our method for conjugate heat transfer and fluid-structure interaction couplings, being two important cases in multiphysics.