3rd int. workshop on high-order cfd methods, kissimmee ... · test case c2.2: summary of results i...
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3rd Int. Workshop on High-Order CFD Methods, Kissimmee, Florida, Jan 3-4, 2015
Summary of the C2.2 test case results: Delta wing at low Re(Test case was named C2.4 up to the 2nd workshop)
Ralf HartmannInstitute of Aerodynamics and Flow TechnologyGerman Aerospace Center
3. Jan 2015 (Updated: 31. March 2015)
1 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2
Laminar flow at M = 0.3, Re = 4000 and α = 12.5◦ around the delta wing
geometry
Reference values(taken from [LH10]):C refd = 0.1658, C ref
l = 0.347.Mach number isosurfaces (left) and slices (right) [LH10]
[LH10] T. Leicht and R. Hartmann. Error estimation and anisotropic mesh refinement for 3d laminar
aerodynamic flow simulations. J. Comput. Phys., 229(19), 7344-7360, 2010.
2 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2
Laminar flow at M = 0.3, Re = 4000 and α = 12.5◦ around the delta wing
Nested hexahedral meshes available on the HioCFD workshop homepage:
I delta.1.msh with 408 cells
I delta.2.msh with 3,264 cells
I delta.3.msh with 26,112 cells
I delta.4.msh with 208,896 cells
3 / 14Summary of the C2.2 test case results
Ralf Hartmann
Summary of test case C2.2
Laminar flow at M = 0.3, Re = 4000 and α = 12.5◦ around the delta wing
Data has been submitted for the 3rd workshop from
I Xiaodong Liu, Yidong Xia, Hong Luo (RDGFLO3D), North Carolina StateUniversity, sequence of own unstructured purely tetrahedral meshes (withsame farfield distance and geometry), DG/rDG, NCState
I Michael Woopen, Aravind Balan, Georg May (AdHoCFD), RWTH Aachen,HioCFD meshes, HDG,Aachen
I Marco Ceze, Krzysztof Fidkowski (XFlow), Uni. of Michigan, HioCFDmeshes and adjoint-based refined meshes, DG,UMich and DG,adj,UMich
.. and will be compared with the data of the 1st and 2nd workshop from
I Ralf Hartmann (PADGE), on HioCFD meshes, DG,DLR
I Tobias Leicht (PADGE), on adjoint-based refined meshes, DG,adj,DLR
I Jun Kudo, Steven R. Allmaras, David L. Darmofal (ProjectX), h-optimizedmeshes, DG,h-opt,MIT
4 / 14Summary of the C2.2 test case results
Ralf Hartmann
Summary of test case C2.2
Reference values
I are taken from [LH10]: C refd = 0.1658, C ref
l = 0.347constant viscosity, isothermal wall boundary condition
5 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Cd vs. h
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.01
Cd
h=1/(number of DoFs per equation)^(1/3)
DLR,DG,Q1DLR,DG,Q2DLR,DG,Q3DLR,DG,Q4NCState,DG,P1NCState,rDG,P1P2Aachen,HDG,Q1Aachen,HDG,Q2Aachen,HDG,Q3Aachen,HDG,Q4UMich,DG,Q1UMich,DG,Q2UMich,DG,Q3Cd_ref[LH10]
6 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Cl vs. h
0.32
0.34
0.36
0.38
0.4
0.42
0.44
0.46
0.01
Cl
h=1/(number of DoFs per equation)^(1/3)
DLR,DG,Q1DLR,DG,Q2DLR,DG,Q3DLR,DG,Q4NCState,DG,P1NCState,rDG,P1P2Aachen,HDG,Q1Aachen,HDG,Q2Aachen,HDG,Q3Aachen,HDG,Q4UMich,DG,Q1UMich,DG,Q2UMich,DG,Q3Cl_ref[LH10]
7 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cd vs. h
0.001
0.01
0.01
Cd
_re
f-C
d
h=1/(number of DoFs per equation)^(1/3)
O(h)O(h^2)
DG,Q1,DLRDG,Q2,DLRDG,Q3,DLRDG,Q4,DLR
DG,P1,NCStaterDG,P1P2,NCState
HDG,Q1,AachenHDG,Q2,AachenHDG,Q3,AachenHDG,Q4,Aachen
DG,Q1,UMichDG,Q2,UMichDG,Q3,UMich
8 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cl vs. h
0.001
0.01
0.1
0.01
Cl_
ref-
Cl
h=1/(number of DoFs per equation)^(1/3)
O(h)O(h^2)
DG,Q1,DLRDG,Q2,DLRDG,Q3,DLRDG,Q4,DLR
DG,P1,NCStaterDG,P1P2,NCState
HDG,Q1,AachenHDG,Q2,AachenHDG,Q3,AachenHDG,Q4,Aachen
DG,Q1,UMichDG,Q2,UMichDG,Q3,UMich
9 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cd vs. h
0.001
0.01
0.01 0.1
Cl_
ref-
Cl
h=1/(number of DoFs per equation)^(1/3)
O(h)O(h^2)
DG,Q1,DLRDG,Q2,DLRDG,Q3,DLRDG,Q4,DLR
DG,P2,adj,DLRDG,P(hp),adj,DLRDG,P1,h-opt,MITDG,P2,h-opt,MITDG,P1,NCState
rDG,P1P2,NCStateHDG,Q1,AachenHDG,Q2,AachenHDG,Q3,AachenHDG,Q4,Aachen
DG,Q1,UMichDG,Q2,UMichDG,Q3,UMich
DG,P1,adj,UMichDG,P2,adj,UMichDG,P3,adj,UMich
10 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cl vs. h
0.001
0.01
0.1
0.01 0.1
Cl_
ref-
Cl
h=1/(number of DoFs per equation)^(1/3)
O(h)O(h^2)
DG,Q1,DLRDG,Q2,DLRDG,Q3,DLRDG,Q4,DLR
DG,P2,adj,DLRDG,P(hp),adj,DLRDG,P1,h-opt,MITDG,P2,h-opt,MITDG,P1,NCState
rDG,P1P2,NCStateHDG,Q1,AachenHDG,Q2,AachenHDG,Q3,AachenHDG,Q4,Aachen
DG,Q1,UMichDG,Q2,UMichDG,Q3,UMich
DG,P1,adj(Cd),UMichDG,P2,adj(Cd),UMichDG,P3,adj(Cd),UMich
11 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cd vs. workunits
0.001
0.01
0.1 1 10 100 1000 10000
Cd
_re
f-C
d
work units
DLR,DG,Q1DLR,DG,Q2DLR,DG,Q3DLR,DG,Q4DLR,DG,P2,adjDLR,DG,P(hp),adjMIT,DG,P1,h-optMIT,DG,P2,h-optNCState,DG,P1NCState,rDG,P1P2Aachen,HDG,Q1Aachen,HDG,Q2Aachen,HDG,Q3Aachen,HDG,Q4UMich,DG,Q1UMich,DG,Q2UMich,DG,Q3UMich,DG,P1,adjUMich,DG,P2,adjUMich,DG,P3,adj
12 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Error in Cl vs. workunits
0.001
0.01
0.1
0.1 1 10 100 1000 10000
Cl_
ref-
Cl
work units
DLR,DG,Q1DLR,DG,Q2DLR,DG,Q3DLR,DG,Q4DLR,DG,P2,adjDLR,DG,P(hp),adjMIT,DG,P1,h-optMIT,DG,P2,h-optNCState,DG,P1NCState,rDG,P1P2Aachen,HDG,Q1Aachen,HDG,Q2Aachen,HDG,Q3Aachen,HDG,Q4UMich,DG,Q1UMich,DG,Q2UMich,DG,Q3UMich,DG,P1,adj(Cd)UMich,DG,P2,adj(Cd)UMich,DG,P3,adj(Cd)
13 / 14Summary of the C2.2 test case results
Ralf Hartmann
Test case C2.2: Summary of results
I There is some spread of workunits taken by different discretization methodsand codes (up to a factor of 500, but much less than in the 2nd workshop).
I HDG is somewhere in middle of the range of DG results (in terms of accuracyper DoFs and workunits).
I For higher accuracy requirements there is a gain (in terms of DoFs andworkunits) of DG(p = 2) over DG(p = 1).
I Due to the non-smoothness of the flow solution the order of convergence onhierarchy of meshes is bounded by 2 (irrespective of the theoretical order ofthe discretization).
I There is not much gain (if at all) in workunits using a global p > 2.
I hp-refinement gives only a small advantage over pure h-refinement for p = 2.
I NCState’s results on their mesh sequence show a larger order of convergencethan the other results on the uniformly refined mesh sequence. This might bedue to the (non-uniformly refined) mesh sequence of NCState having adifferent resolution near the non-smoothnesses than the grids provided.
14 / 14Summary of the C2.2 test case results
Ralf Hartmann