1st International Workshop on High-Order CFD Methods
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1 1st International Worksop on Hig-Order CFD Metods Test Case C1.3: Steady Flow over te NACA0012 Airfoil Georg May, Micael Woopen Graduate Scool AICES, RWTH Aacen January 26, 2012 Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
2 Test Case 1.3: Summary Trends in numerical discretization and relaxation procedures Summary of results Tis report: Not too eavy on statistics (small sample size) 1.3a (subsonic, inviscid): 6 data sets 1.3b (transonic, inviscid): 3 data sets 1.3c (subsonic, viscous): 5 data sets Note: Not all contributions represented (missing data) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
3 Discretization Metods Metod of coice seems to be DG Tis includes many DG-flavors (e.g. CPR-DG) Non-DG submissions: Finite-Volume (1) SBP-SAT (1) Most use fairly standard DG scemes Winner of popularity contest: DG wit BR2 (used by a tird of submissions) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
4 Meses and Fidelity of Results Meses Very many different meses found use provided quad meses self-generated meses (quad, tri, and mixed) Correlation between mes type and fidelity of results not attempted ere Submissions include adaptive metods (goal-oriented) General Remark on Results For subsonic cases: Convergence studies reveal superiority of ig-order approximation Fewer DOFS for same error Lower CPU time for same error Work needs to be done for transonic flow Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
5 Solution Metods Tis is a steady test case! Look for efficient relaxation metods Metod of coice seems to be (damped) Newton / Krylov Almost all use GMRES (one BICGSTAB) No consensus on preconditioners ILU-n Gauss-Seidel Multigrid Important note: We do not compare and evaluate efficiency insufficient number of samples We cannot assume all codes are fully optimized Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
6 Convergence Summary Test Case C1.3a (Subsonic inviscid) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
7 Convergence Towards Trut Solution Do we agree on te trut solution? Trut lift and drag coefficients Average Standard Deviation Drag E E-06 Lift 2.865E E-05 Compare to p=3 solutions Average Standard Deviation Drag E E-05 Lift 2.865E E-05 Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
8 Convergence towards Trut Solution order Mean lift and drag coefficients for eac order on te finest mes approacing te mean reference values Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
9 Convergence Test Case C1.3a (Subsonic Inviscid) 2nd Order 2nd Order (p=1) 2nd Order Gooc Darmofal 2nd Order nd Order Darmofal Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
10 Convergence Test Case C1.3a (Subsonic Inviscid) 3rd Order p=2 3rd Order Darmofal Gooc Darmofal Darmofal 3nd Order rd Order Darmofal Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
11 Convergence Test Case C1.3a (Subsonic Inviscid) 4t Order p=3 4t Order Gooc Svaerd Darmofal Svaerd Svaerd 4t Order t Order Darmofal Svaerd Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
12 Convergence Test Case C1.3a (Subsonic Inviscid) 5t Order p=4 5t Order Svaerd Svaerd 5t Order t Order Svaerd Svaerd Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
13 Convergence Test Case C1.3a (Subsonic Inviscid) 6t Order p=5 6t Order Svaerd Svaerd 6t Order t Order Svaerd Svaerd Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
14 Convergence Summary Test Case C1.3b (Transonic Inviscid) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
15 Convergence Test Case C1.3b (Transonic Inviscid) 2nd Order 2nd order (p=1) 2nd Order Darmofal Darmofal 2nd Order nd Order ( uses p=1..4. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
16 Convergence Test Case C1.3b (Transonic Inviscid) 3rd Order p=2 3rd Order Darmofal Darmofal 3rd Order rd Order ( uses p=1..4. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
17 Convergence Summary Test Case C1.3c (Subsonic Viscous) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
18 Convergence Towards Trut Solution order Mean lift and drag coefficients for eac order on te finest mes approacing te mean reference values Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
19 Convergence Test Case C1.3c (Subsonic Viscous) st Order 1st order (p=0) 1st Order 1st Order st Order c l Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
20 Convergence Test Case C1.3c (Subsonic Viscous) 2nd Order p=1 2nd Order 10 1 Darmofal 10 0 Mavriplis Mavriplis Mavriplis 2nd Order nd Order Mavriplis ( uses p=1..5. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
21 Convergence Test Case C1.3c (Subsonic Viscous) 3nd Order p=2 3rd Order 3rd Order rd Order ( uses p=1..5. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
22 Convergence Test Case C1.3c (Subsonic Viscous) 4t Order p=3 4t Order 4t Order t Order ( uses p=1..5. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
23 Convergence Test Case C1.3c (Subsonic Viscous) t Order p=4 5t Order 5t Order t Order ( uses p=1..5. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
24 Convergence Test Case C1.3c (Subsonic Viscous) t Order p=5 6t Order 6t Order t Order ( uses p=1..5. Tis curve is te same for all values of p) Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
25 Summary of Conclusions Participants use: Predominantly DG Discretization metods Similar Solution metods for te steady problem Higer order pays in terms of work units versus error i.e. for te subsonic cases! Convergence in lift and drag sows considerable scatter Adaptive mes refinement demonstrates advantages Very difficult to establis clear trends Georg May, Micael Woopen 1st International Worksop on Hig-Order CFD Metods
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