Aerodynamic Shape Optimization by means of Sequential Linear Programming Techniques

An optimization framework for aerodynamic design on unstructured meshes has been implemented. It includes a finite volume solver based upon a median-dual discretization, its discrete adjoint, and shape parameterization and mesh moving/deforming algorithms. The framework elements are coupled and linked to a Sequential Quadratic Programming (SQP) optimization algorithm, taken from a library. The framework has been tested and found effective in the design of shock-free airfoils at transonic flow conditions. However, in general, shape optimization is not a rigorous process and many issues (e.g design variable bounds or constraints specifications) require user interaction in order to avoid unfeasible designs. Therefore, especially in the context of expensive aerospace applications, it is desirable to have an optimization procedure capable of achieving near optimal design and allowing the user to interact with the framework in order to gain more insight into the design space. The SQP algorithm, in spite of its effectiveness, limits the designer in using his engineering knowledge to steer the optimization process. A Sequential Linear Programming technique has been investigated as an algorithm more tailored to shape optimization problems in the preliminary design phase. The idea behind this algorithm is very simple: given a non-linear optimization problem (i) perform a linearization around the design point, (ii) solve the linearized problem using a Linear Programming algorithm to obtain a new design point, (iii) linearize around the new design point and solve again the Linear Programming problem until the minimum of the non-linear problem is found. A drawback of the algorithm is that for under-constrained design cases the linearized problem can be unbounded. To overcome this problem the domain resulting from the linearization must be reduced. The definition of the reducing factor is a crucial part in the algorithm and can affect the effectiveness and the efficiency of the optimization. The paper includes a brief introduction to the framework in which the discrete adjoint is addressed in terms of implementation and solution issues. After the introduction, the Sequential Linear Programming algorithm is discussed more in detail and demonstrated on different test cases