1. Remarks on the TAU grid adaptation Thomas Gerhold

2. Concept – initial idea for adaptation tool Introduction A short presentation of the basic concept & restrictions for the local grid refinement is given, because it might be useful for discussions about the adaptation tool. concept for grid refinement restrictions summary

3. Concept – initial idea for adaptation tool Unstructured grids allows for local refinement Flow fields are dominated by local phenomena (stagnation point/line, expansion, shock, separation, wake, vortices) Flow phenomena change with flow conditions One initial grid and local refinement allows to resolve flow phenomena efficiently for varying flow conditions (e.g. for a polar)

4. Concept - automated chain from CAD to solution Initial grids can be generated (more or less) automatically, e.g. by refinement based on surface curvature and other parameters Local refinement based on indicators for flow phenomena allows for an automated process to obtain a final grid for the case- specific flow conditions - overhead for a simulation with local refinement + saving time in initial grid generation (less user-interaction) + improved resolution for the actual flow conditions for a given number of points

5. Concept – local refinement Local grid refinement based on the equi-distribution principle: insert points to equalize maximum differences of the indicator function between neighboured cells Equi-distribution provides the best spatial resolution for a target number of points for a given initial grid and a given indicator function initial grid points inserted points maximum difference

6. Concept – required functionality Handle grid refinement Provide a tool which refines unstructured grids locally based on edges marked for refinement. Define refinement regions Offer build-in indicators for marking edges: default: Pt, Ht, V, Rho Allow the user alternatively to select the refinement locations (e.g. read user-defined sensor-variables, lists for selected elements, adjoint based selection in future)

7. concept – offer choices for the indicator setting Final grid depends on the choice of the indicator (weights) and other parameter settings. Thus, experience to be gained by the users, which settings to use for which use cases. Default setting are certainly not optimal for each case. With the user experiences feedback will show the need for other additional indicators Indicator Pt Indicator V

8. Proof of concept It has been shown for cruise conditions that local grid refinement (using build-in Indicators) lead to an improved solution in comparison to a reference solution Turbulent F6 simulation with 2 adaptation steps from 2 mio to 3.5 mio points (Stab-Paper 1998) Convergence history:

9. restrictions Sizes of refined cells depend on the initial grid and the number of refinement steps. Thus, to resolve a wake far downstream needs several adaptation steps (eventually more than 10), because farfield cell sizes are often 5 orders larger than nearfield cell sizes

10. restrictions (in semi structured layers) No refinement under chopping regions! Indicators not evaluated on wall normal prism-edges: no wall- tangential refinement! Thus, some regions of interest (especially for high lift configurations) can not be refined or not be refined locally!

11. Conclusion summary: Basic concept for grid refinement & restrictions have been presented Experiences: Many applications has shown that adaptation improve results compared to the initial coarse grid solution Potential: Improved indicators, e.g. ongoing work based on adjoint-solutions can make the adaptation more efficient, using the existing infrastructure for local refinement.