Multivariate Design Optimization using the Proper Orthogonal Decomposition Method applied to a Low Reynolds Number Airfoil*

A multivariate design optimization that utilizes the Proper Orthogonal Decomposition (POD) method is presented and applied to the design of a low Reynolds number airfoil. The airfoil shape is described by seven independent design variables. The optimization procedure modifies the airfoil shape such that lift-over-drag is maximized. To reduce the computational expense of the optimization process, the POD method is used. In the POD method, each state variable is approximated with a linear combination of modal coefficients, which are functions of the design variables, and basis functions, which are functions of space. The optimization method is as follows. First, reference solutions using an appropriate CFD solver are computed across the range of design variables at each reference point. The reference points are placed using Latin Hypercube sampling (LHS). Then, a global POD basis is created from all reference points. Finally, the modal coefficients are computed using multivariate interpolation from neighboring points. The final solution is reconstructed using the global POD basis and the interpolated modal coefficients and the lift-over-drag is calculated. The interpolation process is iterated until an optimum is reached.