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- Nordström, Jan, 1953-, et al.
(författare)
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Robust Design of Initial Boundary Value Problems
- 2019
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Ingår i: Uncertainty Management for Robust Industrial Design in Aeronautics. - Cham : Springer. - 9783319777672 - 9783319777665 ; , s. 463-478
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Bokkapitel (refereegranskat)abstract
- We study hyperbolic and incompletely parabolic systems with stochastic boundary and initial data. Estimates of the variance of the solution are presented both analytically and numerically. It is shown that one can reduce the variance for a given input, with a specific choice of boundary condition. The technique is applied to the Maxwell, Euler, and Navier–Stokes equations. Numerical calculations corroborate the theoretical conclusions.
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| 2. |
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| 3. |
- Wahlsten, Markus, 1986-, et al.
(författare)
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Galerkin projection and numerical integration for a stochastic investigation of the viscous Burgers equation : An initial attempt
- 2019
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Konferensbidrag (refereegranskat)abstract
- We consider a stochastic analysis of the non-linear viscous Burgers’ equation and focus on the comparison between intrusive and non-intrusive uncertainty quantification methods. The intrusive approach uses a combination of polynomial chaos and stochastic Galerkin projection. The non-intrusive method uses numerical integration by combining quadrature rules and the probability density functions of the prescribed uncertainties. The two methods are applied to a provably stable formulation of the viscous Burgers’ equation, and compared. As measures of comparison: variance size, computational efficiency and accuracy are used.
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| 4. |
- Wahlsten, Markus, 1986-, et al.
(författare)
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On Stochastic Investigation of Flow Problems Using the Viscous Burgers’ Equation as an Example
- 2019
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Ingår i: Journal of Scientific Computing. - : Springer Science and Business Media LLC. - 0885-7474 .- 1573-7691. ; 81:2, s. 1111-1117
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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