A general purpose discrete adjoint formulation for inviscid two-dimensional fluid dynamic optimization

A general purpose discrete adjoint formulation for robust and efficient design optimization of nozzles in inviscid flow conditions, with different flow solvers, is presented and tested on various nozzle problems. An approximate, dissipative flow solver is used to develop the discrete quasi-time-dependent adjoint equations. The resulting design sensitivities are very robust even in the presence of noise or other non-smoothness associated with objective functions in many high-speed flow problems. The optimization is performed using a sequence of progressively finer grids for the solution of the flow field, together with a progressive optimization, whereby a sequence of a partially converged flow solutions is followed by an optimization step. In order to calculate accurate objective functions, the flow field must be computed by accurate flow solvers. First, the previous adjoint equations are coupled with an accurate in-house flow solver to test the approach on some inverse design problems involving two-dimensional transonic, subsonic and incompressible nozzle flows. The methodology is shown to be robust and highly efficient. Then, the previous design test cases are re-computed coupling the suggested adjoint formulation with commercial flow solvers, without noticing any significant difference in the optimization convergence histories. This evidence prove the employed adjoint formulation to be quite general, because it allows to perform accurate and efficient design optimization using different flow solvers. Finally, the incompressible design test case is re-computed coupling the suggested compressible adjoint formulation with a commercial incompressible flow solver; the successful optimization further substantiates the present discrete adjoint formulation to be a general purpose adjoint formulation, which can even be coupled to incompressible flow solvers.