Adaptive FEMfor Aerospace and
Aeroacoustics Applications
Rodrigo Vilela de Abreu
Niclas Jansson Johan Jansson
Johan Hoffman
Computational Technology Laboratory,CSC/HPCViz,KTH
5
th
ANSAand mETAInternational Conference,Thessaloniki,
57 June,2013.
About us
What do we do?
I
Develop the opensource turbulent ﬂowsolver UNICORN.
I
FEniCS opensource project.
I
MPIIO,parallel meshreﬁnement,dynamic loadbalancing.
I
Adjoint based mesh adaptivity.
I
Linear scalability up to 12,000 cores.
I
Study turbulent ﬂowphenomena with several applications.
I
1 Professor,1 senior researcher,2 postdocs,5 PhDstudents.
Who amI?
I
4
th
year (of 5) PhDcandidate.
I
Use UNICORNto study aerodynamics and aeroacoustics.
I
Separation,airframe noise (landing gear,slatnoise,etc) and
ductacoustics.
Collaboration with ANSA
Workﬂow
Opensource
CAD/mesh generation
Salome
,
Gmsh
,
Netgen
Opensource
flow solver
UNICORN
Opensource
Postprocessing
Visit
,
Paraview
Collaboration with ANSA
Workﬂow
Opensource
CAD/mesh generation
Salome
,
Gmsh
,
Netgen
Opensource
flow solver
UNICORN
Opensource
Postprocessing
Visit
,
Paraview
Difficult to use for complex
geometries...
Collaboration with ANSA
ANSAmesh generation
Fromleft to right...
I
30P30NfromNASA,benchmark workshops BANCI and
BANCII.
I
GulfstreamG550 nose landing gear,also BANCI and BANCII.
I
DLR model airplane,HighLift Prediction Workshop 2.
Collaboration with ANSA
ANSAmesh generation
Fromleft to right...
I
30P30NfromNASA,benchmark workshops BANCI and
BANCII.
I
GulfstreamG550 nose landing gear,also BANCI and BANCII.
I
DLR model airplane,HighLift Prediction Workshop 2.
Adaptive FEMfor turbulent ﬂows
General Galerkin (G2)
I
FEMwith piecewise linear approximation in space and time.
I
Fully unstructured meshes.
I
Timeresolved method where numerical stabilization accounts
for unresolved scales.
I
Simple wall shear stress model based on skin friction,slip
velocity boundary condition,in the spirit of simpler models.
1
I
Adaptive mesh reﬁnement with respect to output of interest
using associated adjoint problemto estimate errors in output.
1
U.Schumann,Subgrid scale model for ﬁnite difference simulations of turbulent ﬂows in
plane channels and annuli.
Adaptive FEMfor turbulent ﬂows
Adjointbased mesh reﬁnement
For
ˆ
U = (U,P) a weak solution,ˆj = (j,q) a solution to a linearized
adjoint problem,and M(
ˆ
U) = ((
ˆ
U,
ˆ
y)) a mean value output,with
ˆ
y a
weight function,we deﬁne the error estimate:
jM(
ˆ
u) M(
ˆ
U)j = j((
ˆ
u
ˆ
U,
ˆ
y))j å
K2T
n
E
K
,
with the error indicator:
for each element K in the mesh T
n
,with stability weights w
i
,i = 1,2.
Adaptive FEMfor turbulent ﬂows
Adjointbased mesh reﬁnement
For
ˆ
U = (U,P) a weak solution,ˆj = (j,q) a solution to a linearized
adjoint problem,and M(
ˆ
U) = ((
ˆ
U,
ˆ
y)) a mean value output,with
ˆ
y a
weight function,we deﬁne the error estimate:
jM(
ˆ
u) M(
ˆ
U)j = j((
ˆ
u
ˆ
U,
ˆ
y))j å
K2T
n
E
K
,
with the error indicator:
for each element K in the mesh T
n
,with stability weights w
i
,i = 1,2.
Adaptive FEMfor turbulent ﬂows
Adjointbased mesh reﬁnement
For
ˆ
U = (U,P) a weak solution,ˆj = (j,q) a solution to a linearized
adjoint problem,and M(
ˆ
U) = ((
ˆ
U,
ˆ
y)) a mean value output,with
ˆ
y a
weight function,we deﬁne the error estimate:
jM(
ˆ
u) M(
ˆ
U)j = j((
ˆ
u
ˆ
U,
ˆ
y))j å
K2T
n
E
K
,
with the error indicator:
for each element K in the mesh T
n
,with stability weights w
i
,i = 1,2.
Adaptive FEMfor turbulent ﬂows
Adjointbased mesh reﬁnement
For
ˆ
U = (U,P) a weak solution,ˆj = (j,q) a solution to a linearized
adjoint problem,and M(
ˆ
U) = ((
ˆ
U,
ˆ
y)) a mean value output,with
ˆ
y a
weight function,we deﬁne the error estimate:
jM(
ˆ
u) M(
ˆ
U)j = j((
ˆ
u
ˆ
U,
ˆ
y))j å
K2T
n
E
K
,
with the error indicator:
error in M(û)
≡
f
(
turbulence,adjoint solution)
for each element K in the mesh T
n
,with stability weights w
i
,i = 1,2.
Adaptive Mesh Reﬁnement
How do we generate the mesh?
Adaptive algorithm
1.For the mesh T
n
:compute primal and adjoint problem.
2.Compute E
K
,K 2 T
n
.
3.Mark 10%of the elements with highest “error indicator” for reﬁnement.
4.Generate the reﬁned mesh T
n+1
,and goto 1.
Example 30P30Nhighlift wing:
Initial mesh:1Mcells.
Mesh after 7 adaptive reﬁnements:6.6Mcells.
)Compare,e.g.,with Imamura et al,16.3Mpoints!
2
2
Imamura,T.,Murayama,M.,Hirai,T.,and Yamamoto,K.,Aeroacoustic Simulations
around 30P30N,JAXA’s Result,” Proceedings for BANCII,2012.
Adaptive Mesh Reﬁnement
Howto choose the reﬁnement target M(
ˆ
u)?
It depends on the application...
I
For aerodynamics,drag,lift or drag+lift.
I
For external aeroacoustics,Lighthill’s analogy.
I
Duct acoustics,pressure drop.
I
...
Adaptive Mesh Reﬁnement
Initial mesh
3
:
3 reﬁnements
:
9 reﬁnements
:
3
Vilela de Abreu et at,Adaptive computation of aeroacoustic sources for a
rudimentary landing gear using Lighthill’s analogy,Proceedings for the 17th
AIAA/CEAS Aeroacoustics Conference,2011.
Adaptive Mesh Reﬁnement
What are the advantages of an adaptively generated
mesh?
I
Mesh captures the relevant ﬂowfeatures.
I
No need for ad hoc meshing.
I
No need for a “mesh study”
4
.
I
Final mesh has “optimal” size.
4
Ahierarchy of meshes is automatically generated by the adaptive algorithmand
ﬂowsolutions are available for all meshes.Moreover,a stop criterion for the algorithm
should be chosen to ensure “mesh convergence”.
Adaptive Mesh Reﬁnement
Mesh captures the relevant ﬂow features...
Adaptive Mesh Reﬁnement
Mesh captures the relevant ﬂow features...
Adaptive Mesh Reﬁnement
Solution on different meshes...
Benchmark results,BANCII
TKE [m2/s2]
Stream wise velocity [m/s]
Stream wise velocity [m/s]
Vorticity [1/s]
In all ﬁgures:left,sim;right,exp.
Benchmark results,BANCII
Mean static pressure coefﬁcient distribution.
Benchmark results,BANCII
Power Spectral Density unsteady pressure.
Benchmark results,HiLiPW2
1.4
1.5
1.6
1.7
x coordinate (m)
8
6
4
2
0
2
4
6
cp
cp for HiLiftPW2 case 2b alpha=21.000000 eta=0.449000
geometry (scaled+translated)
cp num
cp exp
geometry exp (scaled+translated)
Mean static pressure coefﬁcient distribution.
Why ANSA?
Enabling features
I
Easy to cleanup geometries,even for newusers.
I
Batch mesh generation.
I
Precise control of parameters (e.g.leading edge curvature,growth
rate,minmax cell sizes,quality).
I
High quality volume mesh (highly required in our framework
for reﬁnement).
I
...
)Very knowledgeable,efﬁcient and helpful support!Thanks Vangelis!
Unicorn and DOLFIN,open source
http://launchpad.net/unicorn
Acknowledgement
All initial meshes were generated with ANSAby Beta CAE Systems.
The code Saaz was used in “ofﬂine mode” for postprocessing.
5
Financial support from
I
Swedish Foundation for Strategic Research
I
European Research Council
I
Swedish Research Council,Swedish Energy Agency
This work was performed on resources provided by the Swedish
National Infrastructure for Computing (SNIC) at the Center for
HighPerformance Computing (PDC) at KTH.
5
Alden King,Eric Arobone,Scott B.Baden and Sutanu Sarkar,The Saaz Framework for
Turbulent Flow Queries,2011.
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