c3.5 summary: common research model · c3.5 summary: common research model . 3. rd. international...
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C3.5 Summary: Common Research Model
3rd International Workshop on High-Order CFD Methods January 3rd/4th 2015, Kissimmee, Florida updated/corrected after the workshop Tobias Leicht
www.DLR.de • Chart 1
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C3.5: Common Research Model (CRM) Overview
- steady-state RANS case - cruise conditions – transonic flow - wing-body configuration
similar to modern airliner
- experimental data - extensively studied in AIAA Drag Prediction Workshops 4 and 5
numerical data (Finite Volume) from many groups (55 contributions from 22 groups in DPW-5)
- References: - http://commonresearchmodel.larc.nasa.gov - http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw
for comparison figures are taken from DPW-5 summary presentation (http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop5/presentations/DPW5_Presentation_Files/14_DPW5%20Summary-Draft_V7.pdf)
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C3.5: Common Research Model (CRM) CFD setting
Ma=0.85 Re=5×106
target CL=0.5±0.001
- fully turbulent flow, no transition - free air, no wind tunnel effects
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C3.5: Common Research Model (CRM) Meshes
- multi-block structured meshes
from DPW-5 not high-order, not suited for agglomeration to HO-macro-elements
- coarse cubic hexahedral HO-meshes by University of Michigan obtained via agglomeration of linear structured meshes (45 k and) 80 k element meshes, provided on workshop website
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Results (second workshop)
- only two groups with high order codes - only second order solutions (third order adjoint solves for error estimation)
- Marco Ceze, Krzysztof Fidkowski University of Michigan DG, p=1, SA, mesh adaptive results driven by drag adjoint
- Ralf Hartmann DLR DG, p=1, kω, mesh adaptive results driven by (unweighted) residual ind.
- Stefan Langer DLR FV, second order central scheme, (negative) SA, mesh sequence from DPW-5
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Additional results (third workshop)
- Marco Ceze, Krzysztof Fidkowski University of Michigan DG, p=1, SA, mesh adaptive results driven by drag adjoint (respecting the lift constraint)
- Ralf Hartmann DLR DG, p=1, kω, mesh adaptive results driven by
a) (unweighted) residual indicators b) lift adjoint
- Stefan Langer
DLR FV, second order central scheme, (negative) SA, mesh sequence based on global refinement of HOW mesh
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Individual Presentation(s)
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Reference results
- second order node-centered Finite Volume code (Stefan Langer, DLR) - central scheme with upwind-based artificial dissipation - multi-grid based on Galerkin projection - implicit multi-stage RK smoother - target lift via AoA-bisection
- results on DPW-5 meshes - coarse: 660,177 points - fine: 41,231,169 points
- results on HOW-based meshes
- coarse: 79,505 cells - fine: 5,088,320 cells
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Comparison of results Sectional cuts
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Comparison of results Sectional cuts
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DG (DLR) DG (UM) FV (DLR)
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Comparison of results Integral and scalar values
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− drag coefficient − pitching moment coefficient − angle of attack close similarity of plots to DPW-5 summary
− same axis ranges − plotted against
− for second order convergence this yields straight lines
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Comparison of results mesh convergence: pitching moment
DPW-5
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present results
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Comparison of results mesh convergence: pitching moment
DPW-5
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present results
Different axis scale! UM HOW III results corrected after the workshop, discrepancy remains unclear
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Comparison of results mesh convergence: angle of attack
DPW-5
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present results
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Comparison of results mesh convergence: drag
DPW-5
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present results
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Comparison of results mesh convergence: pressure drag
DPW-5
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present results
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Comparison of results mesh convergence: friction drag
DPW-5
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present results
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Comparison of results mesh convergence: drag
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Observations
- (some) DG results are not mesh converged. → Large variation between last two adaptation steps. → FV on DPW meshes shows surprisingly little variation with mesh density.
- Mainly an effect of underlying mesh sequence. - FV results on HOW mesh equally bad.
- Also: error cancellation for pressure drag and friction drag.
- Confirmation of expectations (UM vs. DLR) - Adaptation seems to improve convergence of drag results,
adjoints more effective than unweighted residuals. - Higher computational cost (work units) for UM than DLR at same
degrees of freedom, consistent to results for other cases.
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Conclusions
- Results are reasonable in comparison with DPW-5 results. - DG results (mostly) heading towards the range of FV results.
- Some differences are not clear. - Shock capturing seems to work reasonably well.
- 3D transonic RANS is still challenging for HO (DG) codes. - Results indicate some progress… - … but currently not at higher order.
The present results demonstrate the applicability of DG for this scenario, but they do not show a clear advantage of DG over FV methods.
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