On Stochastic Investigation of Flow Problems Using the Viscous Burgers’ Equation as an Example

Wahlsten, Markus,1986-Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten (author)

We consider a stochastic analysis of non-linear viscous fluid flow problems with smooth and sharp gradients in stochastic space. As a representative example we consider the viscous Burgers’ equation and compare two typical intrusive and non-intrusive uncertainty quantification methods. The specific intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The specific non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are compared in terms of error in the estimated variance, computational efficiency and accuracy. This comparison, although not general, provide insight into uncertainty quantification of problems with a combination of sharp and smooth variations in stochastic space. It suggests that combining intrusive and non-intrusive methods could be advantageous.

NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
Uncertainty quantification; Stochastic data; Polynomial chaos; Stochastic Galerkin; Intrusive methods; Non-intrusive methods; Burgers’ equation

Nordström, Jan,1953-Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten(Swepub:liu)janno11 (author)
Linköpings universitetBeräkningsmatematik (creator_code:org_t)

In:Journal of Scientific Computing: Springer Science and Business Media LLC81:2, s. 1111-11170885-74741573-7691

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