Uncertainty Quantification and Propagation in Numerical Simulations of Flow-Structure Interactions

Uncertainty Quantification and Propagation in Numerical

Simulations of Flow-Structure Interactions

Didier Lucor

Laboratoire de Modélisation en Mécanique UPMC - UMR CNRS 760

Boite 162, 4 place Jussieu Tel: 33 (0)1 44 27 87 12

75252 Paris Cedex 05 Fax: 33 (0)1 44 27 52 59

France email:

[email protected]

DNS of 3D turbulent flow past a rigid cylinder at

Re=10000

Re=10000 DoF: 200 Millions Number of Processors: 512 Use of multi-level parallelism (MPI-MPI or OpenMP-MPI)

Dong & Karniadakis, JFS, (2005).

Linear shear case

Exponential shear case

Uniform case

DNS-Experiments comparison of a turbulent flow past a rigid stationary

cylinder

Re=3900

Energy spectrum based on the transverse velocity component of the flow field in the wake (x/D=7).

DNS: Ma & Karniadakis, JFM, (2000).Experiments: Ong & Wallace, Experiments in Fluids (1996).

Sources of uncertainty

Parameters, simulation constants, material properties

Transport coefficients, physical properties

geometry

Boundary conditions, initial conditions

Physical laws, numerical schemes

Random inflow condition (stochastic process)

Uncertain boundary conditions

Random structural

parameters

generalized Polynomial Chaos (gPC)

Not limited to a Gaussian distribution!

There exists a unique correspondence between the PDF of the stochastic

input and the weighting function of the orthogonal polynomials.

Inner product:

Polynomials choice

Uniform distribution approximation using the Gaussian/Hermite Chaos.

gPC summary

with

: random space dimension

: highest polynomial order

Example:

: Gaussian distribution

: Hermite polynomials

N=2; P=2

not limited to Gaussian distributions!

Mean:Varianc

e:

Uncertainty at the inflow velocity boundary condition

Deterministic forced motion

Noisy inflow past an oscillating cylinder

30%

20%

10%

0%

σU

Dramatic change in the vortices arrangement in the wake.

The shedding-mode switches from a (P+S) pattern to a (2S) mode in the presence of uncertainty.

For a given level of uncertainty, the change is more pronounced for higher Reynolds numbers.

Lucor & Karniadakis, Phys. Rev. Lett. (2005).

Instantaneous vorticity field RMS values

Lucor & Karniadakis, PRL, (2005).

Uncertainty in flow-structure interaction Objectives:

Uncertainty propagation and quantification in flow-structure interactions coupled phenomena.

Sensitivity of the solution to the different random inputs. Stochastic response surfaces.

Reliability and robustness of the structures to random perturbations.

Technical approach:Intrusive and non-intrusive use of the generalized Polynomial Chaos; Karhunen-Loève stochastic process representation.

Development of efficient and accurate stochastic numerical codes DNS-gPC & LES-gPC.

Large-scale parallel numerical simulations.

• Applications:Different sources of uncertainty:

- advection velocity (écoulement aux bords) - Source term - Initial conditions

- physical properties of the structure - geometry - Boundary conditions

Incompressible 2D & 3D turbulent flows in complex stationary or moving geometry.

Linear & nonlinear structural models, higher Re numbers.

Turbulence et simulation aux grandes échelles (LES)

Objectifs:Propager et quantifier les incertitudes dans les petites échelles

(sous-maille) de l'écoulement.

Quel est l’espace engendré par un modèle sous-maille? Quelles sont les quantités statistiques les moins sensibles (les plus robustes) donc les plus fiables?

Construction de nouveaux modèles sous-maille. Etude de la sensibilité de la solution aux différents paramètres des modèles sous-maille.

Approche technique:Utilisation intrusive ou non-intrusive des polynômes de chaos

généralisés et représentation de Karhunen-Loève.

Ecriture d’un code de calcul stochastique (LES-PCg) et comparaison/validation avec un code (DNS-PCg) existant.

Calculateurs parallèles haute performance.

Applications:Ecoulements turbulents ouverts (de type sillage) et écoulements

pariétaux à haut nombre de Reynolds.