This paper discusses the use of control theory for optimum design of aerodynamic configurations. Examples are presented of the application of this msethod to the reduction of shock induced pressure drag on airfoils in two-dimensional transonic flow.

available at: https://www.grc.nasa.gov/hiocfd/workshop-results/ Case C1.2b: Flow over the NACA0012 airfoil transonic case Andrea Ferrero∗and Francesco Larocca† Department of Mechanical and Aerospace Engineering Politecnico di Torino, Italy

The connection between gas dynamics and differential geometry is discussed. Some history of boundary value problems for systems of conservation laws is first given. Then the mathematical formulation of compressible gas dynamics, especially the subsonic and transonic flows past an obstacle (such as an airfoil), is provided. Some recent results on transonic flow from viscous approximation and com...

A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant γ ∈ [1, 3). This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound uniformly away from cavitation for the viscous approximate velocity fields. Mathematical entropy pairs...