Goal-oriented error estimation and hp-adaptive mesh refinement for aerodynamic flows

Abstract

We present adjoint-based techniques to estimate the error of a numerical flow solution with respect to a given target quantity like an aerodynamic force coefficient. This estimate can be used to judge the overall accuracy of a computation, to enhance the computed value of the target quantity and to drive a solution-adaptive mesh refinement process. The error estimation procedure is extended to multiple target functionals. The discontinuous ansatz spaces of the DG discretization allow for both element subdivision as well as a local increase of polynomial degrees for increasing the flow resolution. Targeting optimal rates of convergence, a smoothness estimation based on a truncated Legendre series expansion of the solution is employed to locally select the more promising strategy. Numerical examples for inviscid, laminar viscous and turbulent viscous flows including a three element airfoil high lift configuration and a wing-body aircraft configuration demonstrate the efficiency of the proposed algorithms.