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An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems


Abgrall, Rémi; Congedo, Pietro Marco; Geraci, Gianluca; Iaccarino, Gianluca (2015). An adaptive multiresolution semi-intrusive scheme for UQ in compressible fluid problems. International Journal for Numerical Methods in Fluids, 78(10):595-637.

Abstract

This paper deals with the introduction of a multiresolution strategy into the semi-intrusive scheme, recently introduced by the authors, aiming to propagate uncertainties in unsteady compressible fluid applications. The mathematical framework of the multiresolution setting is presented for the cell-average case, and the coupling with the semi-intrusive scheme is described from both the theoretical and algorithmic point-of-view. Some reference test cases are performed to demonstrate the convergence properties and the efficiency of the overall scheme: the linear advection problem for both smooth and discontinuous initial conditions, the inviscid Burgers equation, and an uncertain shock tube problem obtained by modifying the well-known Sod shock problem. For all the cases, the convergence curves are computed with respect to semi-analytical (exact) solutions. In the case of the shock tube problem, an original technique to obtain a reference highly-accurate numerical stochastic solution has also been developed.

Abstract

This paper deals with the introduction of a multiresolution strategy into the semi-intrusive scheme, recently introduced by the authors, aiming to propagate uncertainties in unsteady compressible fluid applications. The mathematical framework of the multiresolution setting is presented for the cell-average case, and the coupling with the semi-intrusive scheme is described from both the theoretical and algorithmic point-of-view. Some reference test cases are performed to demonstrate the convergence properties and the efficiency of the overall scheme: the linear advection problem for both smooth and discontinuous initial conditions, the inviscid Burgers equation, and an uncertain shock tube problem obtained by modifying the well-known Sod shock problem. For all the cases, the convergence curves are computed with respect to semi-analytical (exact) solutions. In the case of the shock tube problem, an original technique to obtain a reference highly-accurate numerical stochastic solution has also been developed.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:10 August 2015
Deposited On:03 Feb 2016 10:26
Last Modified:08 Dec 2017 18:20
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0271-2091
Publisher DOI:https://doi.org/10.1002/fld.4030

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