Ralf Hartmann
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, see
e.g. [HH02,Har06].

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, see
[HH03,Har07a].

Numerical results shown in this talk include 2d and 3d aerodynamic
flows.


[HH02] R. Hartmann and P. Houston. Adaptive Discontinuous Galerkin
Finite Element Methods for the Compressible Euler
Equations. J. Comput. Phys. 183: 508-532, 2002.
 
[HH03] R. Hartmann and P. Houston. Goal-Oriented A Posteriori Error
Estimation for Multiple Target Functionals. In T.Y. Hou and E. Tadmor,
editors, Hyperbolic Problems: Theory, Numerics, Applications,
pp. 579-588, Springer, 2003.

[Har06] Ralf Hartmann. Adaptive discontinuous Galerkin methods with
shock-capturing for the compressible Navier-Stokes
equations. Int. J. Numer. Meth. Fluids 51(9-10): 1131-1156, 2006.

[Har07] Ralf Hartmann. Multi-target error estimation and adaptivity in
aerodynamic flow simulations. SIAM J. Sci. Comput. (2007). Submitted.