Chris Lacor Dept Mechanical Engineering

Chris Lacor

Description

Chris Lacor Dept. Mechanical Engineering Vrije Universiteit Brussel With thanks to: Dr. S. Smirnov, Ir. Ch. Vandenhaute, Ir. M. Raes, Ir. G. Onorato Intrusive Polynomial Chaos for the Compressible Navier-Stokes Equations

• input uncertainties


• polynomials


• compressible navier-stokes


• uncertain input parameters


• pc decomposition


• basis functions


• gramm-schmidt procedure


• ??? ?


• intrusive approach

Sujets

• Polynomial
• Basis function

Informations

• Publié par: pefav
• Nombre de lectures: 16
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Intrusive Polynomial Chaos for the
Compressible Navier+Stokes
Equations

Chris Lacor
Dept. Mechanical Engineering
Vrije Universiteit Brussel

With thanks to: Dr. S. Smirnov, Ir. Ch. Vandenhaute, Ir. M.
Raes, Ir. G. Onorato

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Polynomial Chaos

Framework

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NODESIM European STREP project 1/11/06+1/03/10

WP3.3: Polynomial Chaos Methods

– TUD:non+intrusive approach

– VUB:intrusive approach

Symposium on Accuracy and Uncertainty in Flow Simulations, ONERA, Chatillon, December 3, 2010

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Polynomial Chaos

PC method relies on a probabilistic
framework.
Uncertain input parameters are modelled
as stochastic variables (or fields) with
known distributions (PDF).
For each stochastic variable a new
dimension ξ is introduced
Solution is sought in a form of PC
decomposition.
A set of orthogonal multidimensional
polynomials ψ is used as basis functions.
The polynomial type depends on the PDF
of the uncertainty, see further
The deterministic coefficients are derived
by Galerkin projection of the governing
equations.
The resulting set of equations is coupled
due to non+linear terms in the Navier+
Stokes equations.

r1r(x,t,x(q!,...,x(q!!
1n
u1u(x,t,x(q!,...,x(q!!
1n
p1p(x,t,x(q!,...,x(q!!
1n

N
∑k k1n
r(x,t,q!1r(x,t!Y(x,...,x!
k10
N
∑k k1n
u(x,t,q!1u(x,t!Y(x,...,x!
k10
N
∑k k1n
p(x,t,q!1p(x,t!Y(x,...,x!
k10

Symposium on Accuracy and Uncertainty in Flow Simulations, ONERA, Chatillon, December 3, 2010