A discrete adjoint-based approach for airfoil optimization on unstructured meshes

A technique for developing and implementing discrete adjoint methods for airfoil aerodynamic optimization problems on unstructured meshes is presented. Two issues in previous discrete adjoint methods are discussed: the total computational cost is still dependent on the number of design variables in previous discrete adjoint formulation based on flow adjoint equations; and the lengthy and error-prone implementation is usually required to develop adjoint codes. For the first question, the adjoint of the object function is constructed by linearizing each procedure of the entire optimization problem and transposing the total linearization so the computational time required to evaluate the gradient is independent of the number of design variables. For the second question, an automatic differentiation tool is applied selectively to the development of the adjoint code so that a "black-box" application of automatic differentiation tool is avoided and the complexity involved in the development and implementation of discrete adjoint methods is reduced. The inverse design and the constrained optimization results demonstrate the efficiency of the present approach.