The aim of the project is to optimize the angle of one element with respect to the others in a 4-element airfoil configuration. This geometric configuration occurs for example during the landing phase of the flight of an airplane.
The flow around the airfoil is computed using the NSC2KE code written by Bijan Mohamadi which computes either Euler or compressible Navier-Stokes solutions with or without turbulence models. The code uses an explicit time scheme of fourth order and finite volume and finite element methods. Turbulence is modeled by the k-epsilon model using either a two layer technique or wall laws. Later an implicit time stepping scheme will alos be incorporated.
For each given angle the mesh is modified in such a way that only nodes near the turning airfoil element are moved. All nodes having a certain distance are not moved, and no nodes are added. Therefore the computational effort is minimal. The mesh transformation is constructed in such a way that the mesh remains conformal. Furthermore the transformation is differentiable with respect to the angle. The construction of this remeshing mapping is one aim of the project.
The aim of the optimization part is to find the sensitivity of the drag and lift coefficient with respect to the angle. For this purpose computations for different angles will be performed. The next goal is to apply the automatic differentiation package ADIFOR to the program to compute the derivative of the cost functional with respect to the angle. A comparison with a finite difference derivative will be performed. Finally a optimization process will be utilized to get the optimal angle. For this purpose an optimization routine of BFGS type will be used.
All computations will first be carried out for stationary Euler equations. After that the compressible Navier-Stokes equations and eventually additional turbulence models can be considered.