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Adaptive Discontinuous Galerkin methods in aerodynamic flow simulations

Important quantities in aerodynamic flow simulations are the drag, 
lift and moment coefficients. Error estimation and goal-oriented 
refinement approaches have been developed for the accurate and 
efficient computation of single force coefficients. These approaches 
are based on computing an adjoint solution related to each of the 
force coefficients under consideration. The resulting goal-oriented 
adaptively refined meshes are specifically tailored to the accurate 
computation of the force coefficient under consideration. 
 
This approach has been extended 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 computation of one adjoint and one 
adjoint-adjoint solution. This way only two auxiliary problems are 
required irrespective of the number on target functionals. 
 
Numerical results shown in this talk include 2d and 3d aerodynamic 
flows.