The preliminary design phase of any engineering project is characterized by computationally efficient low-fidelity predictive modeling to inform early-stage design choices. It is essential to have fast, efficient tools for preliminary analysis in order to maximize the amount of time that can be allocated to the detailed design phase, where high-fidelity models must be used to determine design parameters as accurately as possible.

Much of the relevant analysis applicable to engineering systems is described by partial differential equations, to which the analytical solution is known for a very small class of problems. Instead we resort to compuational methods. One of the most common ways of approximating the solution to a partial differential equation in engineering applications is the finite element method. However, this method and other like it introduce a substantial computational bottleneck in the design process because of their indirect link with the geometric representation of engineering designs. The recently developed field of isogeometric analysis shows great promise due to its ability to circumvent the design-to-analysis bottleneck inherent in conventional finite element methods. More recently still, isogeometric analysis has been utilized to perform shape optimization, providing the potential to eliminate the design-analysis loop altogether. Low-fidelity automatic optimization routines offer to preliminary design the distinct advantage of replacing heuristic human-guided design iteration with mathematically informed iteration toward the optimal design for a system.

In this thesis we propose a novel method for the analysis of an airfoil in high Reynolds number sub-sonic flow as a tool for early stage aircraft design. The geometry of the airfoil is left arbitrary and the airfoil may consist of multiple distinct bodies. We investigate the validity of the method and apply the method to a surrogate optimization problem.