An Aerodynamic Optimization Method Based on the Inverse Problem Adjoint Equations

An adjoint optimization method, based on the solution of an inverse flow problem, is proposed. Given a certain performance functional, it is necessary to find its extremum with respect to a flow variable distribution on the domain boundary, for example, pressure. The adjoint formulation delivers the functional gradient with respect to such a flow variable distribution, and a descent method can be used for optimization. The flow constraints are easily imposed in the parameterization of the distributed control, and therefore those problems with several strict constraints on the flow solution can be solved very efficiently. Conversely, the geometric constraints are imposed either by additional partial differential equations, or by penalization. By adequately constraining the geometric solution, the classical limitations of the inverse problem design can be overcome. Several examples pertaining to internal flows are given.