Book Description

The goal of our research under AFOSR sponsorship is to develop mathematical procedures which can be used to arrive at optimum, or near optimum, aerodynamic shapes by merging techniques from computational fluid dynamics and control theory. With this in mind we have continued to work in two main topics: Development of high resolution shock capturing schemes with low numerical diffusion. Since last year the symmetric limited positive (SLIP) and upstream limited positive (USLIP) schemes have been improved by the introduction of a new flux limiter which guarantees positivity while maintaining good accuracy in smooth flow regions. A comprehensive theory has also been developed for design of numerical fluxes which guarantee stationary discrete shocks with a single interior point. Aerodynamic shape optimization by boundary control progress in aerodynamic shape optimization has been realized on two fronts. First the method has been successfully implemented for two-dimensional lifting potential flows using a general finite volume scheme with numerically generated grids. Secondly, the method has been successfully implemented for three-dimensional wing design using the Euler equations. (AN).