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On Stochastic Investigation of Flow Problems Using the Viscous Burgers’ Equation as an Example
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 81, no 2, p. 1111-1117Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2019. Vol. 81, no 2, p. 1111-1117
Keywords [en]
Uncertainty quantification; Stochastic data; Polynomial chaos; Stochastic Galerkin; Intrusive methods; Non-intrusive methods; Burgers’ equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-161049DOI: 10.1007/s10915-019-01053-7ISI: 000491440200020OAI: oai:DiVA.org:liu-161049DiVA, id: diva2:1362208
Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2019-11-05

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