3rd int. workshop on high-order cfd methods, kissimmee ... · test case c2.2: summary of results i...

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.


Ralf Hartmann

Test case C2.2


Nested hexahedral meshes available on the HioCFD workshop homepage:

I delta.1.msh with 408 cells

I delta.2.msh with 3,264 cells




Ralf Hartmann

Summary of test case C2.2


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


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


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]


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


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]


Ralf Hartmann

Test case C2.2: Error in Cd vs. h

0.001

0.01

0.01

Cd

_re

f-C

d


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


Ralf Hartmann

Test case C2.2: Error in Cl vs. h

0.001

0.01

0.1

0.01

Cl_

ref-

Cl


O(h)O(h^2)


DG,P1,NCStaterDG,P1P2,NCState

HDG,Q1,AachenHDG,Q2,AachenHDG,Q3,AachenHDG,Q4,Aachen



Ralf Hartmann

Test case C2.2: Error in Cd vs. h

0.001

0.01

0.01 0.1

Cl_

ref-

Cl


O(h)O(h^2)


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,P1,adj,UMichDG,P2,adj,UMichDG,P3,adj,UMich


Ralf Hartmann

Test case C2.2: Error in Cl vs. h

0.001

0.01

0.1

0.01 0.1

Cl_

ref-

Cl


O(h)O(h^2)


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,P1,adj(Cd),UMichDG,P2,adj(Cd),UMichDG,P3,adj(Cd),UMich


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


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)


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.


Ralf Hartmann

3rd int. workshop on high-order cfd methods, kissimmee ... · test case c2.2: summary of results i...

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