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

SL Rasch Architects Specialised in special buildings and lightweight structures

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

Virtual Try-Out Space VTOS

Setup - Model

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

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.

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

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

Original Study PAM-FLOW Different meshes

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

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 16-2-1 64 cores: coefficients 32-2-1 in X-Y-Z)

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

OpenFOAM Study

OpenFOAM Study 15 s

OpenFOAM Study

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

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

FLUENT Study