1. A study of the Butterfly-Effect for Massively Separated Flows using OpenFOAM®
Dr. Alexander Michalski, SL-Rasch GmbH
Dr. Ries Bouwman, ESI Group
7th OpenFOAM Workshop

2. SL Rasch
Architects
Specialised in special buildings and lightweight structures

3. ESI Worldwide Operations
Headquarters in Paris, France
Offices in more than 30 countries
Average Headcount: +900 people
Over 200 Scientists
WW Revenue 2010: ~100 M€
Paris, France
Eschborn, Germany
Pilsen, Czech Republic
Farmington Hills, MI
Beijing, China
Tokyo, Japan

4. Virtual Try-Out Space
VTOS

5. Setup - Model

6. Setup – Inlet Profile
A wind-type velocity profile was applied at the inlet, with a law of:
v(z) = 21.1 (z/10)^0.26, in m/s

7. Setup – Post-Processing
11 points were monitored:
3 points 5 meters upstream of the cube, at +/-20m and 0 in Y, and at 30m in Z.
4 points 5m downstream of the cube, at +/-5m and +/-15m in Y, and at 30m in Z.
4 points upstream of umbrella at 60m in X, at +/-5m and +/- 15m in Y, and at 31m in Z.

8. PAM-FLOW
Physics:
Compressible and incompressible NS solver (transient and steady flow)
Turbulence models: Smagorinsky SGS (LES), K-epsilon, Spalart-Almaras, Baldwin-Lomax
Law of the wall or no-slip walls (with semi-structured boundary layer mesh)
Moving bodies (6-DOF rigid bodies, FSI)
Boundary fitted model: ALE grid and automatic remeshing
Embedded mesh
Highly accurate numerical schemes, both in time and space
Spatial discretisation: Edge-based finite-element and explicit/implicit NS solver, Adaptive mesh refinement
Temporal discretisation: Explicit schemes (compressible flow), Implicit pressure projection explicit scheme (incompressible), Implicit matrix free LU-SGS (compressible and incompressible flow)
DMP and SMP (hybrid) parallel runs.
FSI: MPI coupling with VPS (PAM-CRASH)
Main applications: Aeroacoustic sources characterization, Fluid Structure Interaction

9. Original Study PAM-FLOW
Same mesh, different number of domains

10. Original Study PAM-FLOW
Different meshes

11. Original Study PAM-FLOW
Conclusions
For different number of domains, very small differences at beginning of run grow progressively to state of total dissimilitude
Actual (deterministic) instantiation completely different
Mean loads remain similar
Upstream of cube no differences
Butterfly Effect
Even very small (roundoff) errors can have a pronounced effect on actual deterministic instantiation of a flowfield
Important if mean flow field is less important than actual (maximum) field

12. OpenFOAM High quality mesh generated using VisCART
ESI proprietary cartesian automatic mesher
snappyHexMesh not sufficient quality for umbrella structure
Simulation performed with OpenFOAM 2.1
On RedHat Linux
LES
Smagorinsky Subgrid Scale model
1.800 sec real time, time step of 5msec
Max Courant number of 2.0
Flow field initialised from a static flow
0 m/s in all directions
Simulation was done with 3 SIMPLE partitions in X-Y-Z
8 cores: coefficients 4-2-1
32 cores: coefficients
64 cores: coefficients in X-Y-Z)

13. Total Mesh size: 910k cells
VisCART mesh
Total Mesh size: 910k cells

14. OpenFOAM Study

15. OpenFOAM Study
15 s

16. OpenFOAM Study

17. OpenFOAM Study
Although the instantaneous forces/moments as well as flow pictures are different, the average flow fields are very similar.

18. Conclusion Same effect seen with OpenFOAM as with PAM-FLOW Reason:
Irrespective of wind data
Irrespective of transient or steady state run
Effect depends on number of domains
Effect depends on memory preconditioner
Reason:
inner products of very long vectors that are distributed among domains are required
Order for required additions affects iterative solver
Leads to different instantiations with different number of domains

19. FLUENT Study