A general use adjoint formulation for compressible and incompressible inviscid fluid dynamic optimization

Abstract

A discrete adjoint formulation with an ad hoc flow solver has been recently developed and tested on transonic inviscid flow optimization problems. In the present paper the formulation is extended to various compressible flow solvers as well as to a solver for incompressible flows. An approximate, dissipative flow solver is used to develop the discrete quasi-time-dependent adjoint equations. The design problem employs a progressive optimization, i.e., a sequence of operations, containing a partially converged flow solution, followed by an adjoint solution followed by an optimization step. The procedure is performed using a sequence of progressively finer grids. The sensitivity derivative variations are limited to preserve the smoothness of the progressive procedure. First, the adjoint equations are coupled with an accurate in-house flow solver to test the approach on some inverse design problems involving two- and three-dimensional supersonic, transonic, subsonic and incompressible flows. Then, the previous design test cases are re-computed coupling the extended adjoint formulation with commercial and open source flow solvers, without noticing any relevant difference in the optimization convergence histories. Finally, incompressible design test cases are successfully computed coupling the extended adjoint formulation with a commercial solver for incompressible flows. The extended compressible adjoint formulation appears to have a wide application, insofar as it allows to perform accurate and efficient design optimization using different flow conditions, different flow solvers and even a solver for incompressible flows.