Multitarget Error Estimation and Adaptivity in Aerodynamic Flow Simulations

Important quantities in aerodynamic flow simulations are the aerodynamic force coefficients including the pressure induced and the viscous stress induced drag, lift, and moment coefficients. In addition to the exact approximation of these quantities it is of increasing importance, in particular in the field of uncertainty quantification, to estimate the error in the computed quantities. In recent years a posteriori error estimation and goal-oriented refinement approaches have been developed for the accurate and efficient computation of single target quantities. The current approaches are based on computing an adjoint solution related to each of the specific target quantities under consideration. In this paper we extend this approach to the accurate and efficient computation of multiple target quantities. Instead of computing multiple adjoint solutions, one for each target functional, the new approach is based on the solution to one discrete adjoint problem and one discrete error problem. This way only two auxiliary problems are required irrespective of the number of target functionals. The practical performance of this approach is demonstrated for a laminar compressible flow. In particular, the proposed approach is compared to the standard approach of error estimation and goal-oriented refinement as well as to residual-based refinement. The performance of the algorithms is measured in terms of computing resources required for meeting industrial as well as academic accuracy requirements on the computed force coefficients.