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

Markus Wahlsten, Jan Nordström

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1111-1117
Number of pages7
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - 1 Nov 2019
Externally publishedYes


  • Burgers’ equation
  • Intrusive methods
  • Non-intrusive methods
  • Polynomial chaos
  • Stochastic Galerkin
  • Stochastic data
  • Uncertainty quantification

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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