Aerodynamic shape optimization by means of sequential linear programming techniques

A Sequential Linear Programming technique, known as the method of centers, is the driver of an aerodynamic shape optimization framework on unstructured meshes. The first order information required by this technique, functional values and their gradients, are computed by a median-dual flow/adjoint solver which is coupled to an analytical shape parameterization. Functional and geometric constraints are easily handled by the algorithm which appears to be very effective in obtaining efficiently near-optimal designs. Shape optimization results are presented for transonic as well as supersonic flows involving appreciable shape deformations

Development of the Discrete Adjoint for a Three-Dimensional Unstructured Euler Solver

The discrete adjoint of a reconstruction-based unstructured finite volume formulation for the Euler equations is derived and implemented. The matrix-vector products required to solve the adjoint equations are computed on-the-fly by means of an efficient two-pass assembly. The adjoint equations are solved with the same solution scheme adopted for the flow equations. The scheme is modified to efficiently account for the simultaneous solution of several adjoint equations. The implementation is demonstrated on wing and wing–body configurations

Adjoint-based aerodynamic shape optimization on unstructured meshes

In this paper, the exact discrete adjoint of an unstructured finite-volume formulation of the Euler equations in two dimensions is derived and implemented. The adjoint equations are solved with the same implicit scheme as used for the flow equations. The scheme is modified to efficiently account for multiple functionals simultaneously. An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to algorithms for constrained optimization, is tested on airfoil design cases involving transonic as well as supersonic flows. The effect of some approximations in the discrete adjoint, which aim at reducing the complexity of the implementation, is shown in terms of optimization results rather than only in terms of gradient accuracy. The shape-optimization method appears to be very efficient and robust