Improved lift and drag estimates using adjoint Euler equations

Abstract

This paper demonstrates the use of adjoint error analysis to improve the order of accuracy of integral functionals obtained from CFD calculations. Using second order accurate finite element solutions of the Poisson equation, fourth order accuracy is achieved for two different categories of functional in the presence of both curved boundaries and singularities. Similarly, numerical results for the Euler equations obtained using standard second order accurate approximations demonstrate fourth order accuracy for the integrated pressure in two quasi-1D test cases, and a significant improvement in accuracy in a two-dimensional case. This additional accuracy is achieved at the cost of an adjoint calculation similar to those performed for design optimization.