Non-intrusive polynomial chaos method applied to problems incomputational fluid dynamics and a comparison with POD

S. Hijazi, G. Stabile,A. Mola, G. Rozza

MathLab, Mathematics Area, SISSA InternationalSchool for Advanced Studies, Trieste, Italy

19/07/2017

Physical problem

1. Introduction• Angle of attack for an airfoil.• Focus on computing the lift coefficient as an output of interest.• Uncertainty quantification using non-intrusive PCE.• Parameters are velocity magnitude and angle of attack.• Data generated randomly using Latin Hypercube samplingapproach.

ρ

Umax

αmax

Velocity magnitude

ρ

Angle of attack

ζ

ρ

αmax

Lift Coefficient

Fluid Dynamics Simulation

1/ 2 S. Hijazi, G. Stabile, A. Mola, G. Rozza Reduced order methods for CFD problems

Reduced order methods for CFD problems with uncertainty

2. The Full Order Model• The Finite Volume numerical discretization is used for theNavier-Stokes equations.

• OpenFOAM is used as the high order solver.3. The Reduced Order Model• POD-Galerkin ROM for Finite Volume• The in-house developed ITHACA-FV open source library has beenused to build and solve the reduced order model.

• Supremizer approach for stabilizing the pressure• Results : Lift coefficient reconstructed using both POD and PCE

-40 -30 -20 -10 0 10 20 30 40

Angle of attack in degrees

-1.5

-1

-0.5

0

0.5

1

1.5

Lift coeffic

ent

Reconstruced lift coefficent vs High Fidelity one

High Fidelity

POD Reconstructed

-40 -30 -20 -10 0 10 20 30 40

Angle of attack in degrees

-1.5

-1

-0.5

0

0.5

1

1.5

Lift coeffic

ients

Reconstruced PCE output vs orginal one

Original

PCE Reconstructed

2/ 2 S. Hijazi, G. Stabile, A. Mola, G. Rozza Reduced order methods for CFD problems