Adjoint Error Correction for Integral Outputs

Abstract

These lecture notes begin by observing that in many cases the most important engineering outputs of CFD calculations are one or two integral quantities, such as the lift and drag. It is then explained that the solution to an appropriate adjoint problem gives the effect of numerical approximations on the output functional of interest, facilitating the calculation of more accurate functional estimates. The theory is presented for both linear and nonlinear differential equations, incorporating a range of numerical examples illustrating the ability to obtain answers with twice the order of accuracy of the underlying numerical solution.