Modern Aerodynamic Methods for Direct and Inverse Applications

Chapter 4General Analysis and Inverse Methods for Aerodynamic Modeling

Two types of formulations appear in aerodynamics. The first describes “analysis,” “forward” or “direct” problems, in which properties like surface pressure, lift and drag are sought, when airfoil or wing geometries are specified. The second class of problems, referred to by “inverse,” “design” or “indirect” designations, aims at predicting the geometries that induce prescribed surface pressure distributions (such formulations provide improved designer control over aircraft lift and moment, boundary layer stability, turbulent transition, and so on). Historically, aerodynamicists have focused on analysis problems, which are “directly” solved (in a single pass with, say an iterative relaxation method). But direct need not imply simplicity. In fact, solution methods developed over the past decades range from not-so-obvious trigonometric series due to Glauert, to lifting line and lifting surface methods due to Prandtl, and to numerical panel approaches developed by aerospace companies since the 1970s – to the vast array of modern computational tools solving full potential, inviscid Euler and viscous Navier-Stokes flows past vehicular shapes in all their geometric complexity. It is not our purpose to survey these accomplishments. Instead, we wish to address certain aspects of the inviscid inverse problem that are mathematically interesting, advantageous from the perspective of numerical implementation, and significant ...