On Adjoint Equations for Error Analysis and Optimal Grid Adaptation in Cfd

This paper explains how the solutions of appropriate adjoint equations can be used to estimate the errors in important integral quantities , such as lift and drag, obtained from CFD computations. These error estimates can be used to obtain improved estimates of the integral quantities, or as the basis for optimal grid adaptation. The theory is presented for both nite volume and nite element approximations. For a node-based nite volume discretisation of the Euler equations on unstructured grids, the adjoint analysis makes it possible to prove second order accuracy. A superconvergence property is proved for a nite element discretisation of the Laplace equation, and references are provided for the extension of the analysis to the convection/diiusion and incompressible Navier-Stokes equations. This paper was presented at the symposium Computing the Future II: Advances and Prospects in Computational Aerodynamics to honour the contributions of Prof. Earll Murman to CFD and the aerospace community.