Adaptive anisotropic stochastic discretization schemes for uncertain conservation laws

Julie Tryoen*, Olivier Le Maitre, Alexandre Ern

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

This paper deals with the design of adaptive anisotropic discretization schemes for conservation laws with stochastic parameters. A Finite Volume scheme is used for the deterministic discretization, while a piecewise polynomial representation is used at the stochastic level. The methodology is designed in the context of intrusive Galerkin projection methods with Roe-type solver. The adaptation aims at selecting the stochastic resolution level with regard to the local smoothness of the solution in the stochastic domain. In addition, the stochastic features of the solution greatly vary in the space and time so that the constructed stochastic approximation space depends on space and time. The overall method is assessed on the stochastic Burgers equation with shocks, showing significant computational savings.

Original languageEnglish (US)
Title of host publicationASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, FEDSM2010
Pages2941-2956
Number of pages16
EditionPARTS A, B AND C
DOIs
StatePublished - Dec 1 2010
EventASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting, FEDSM 2010 Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels - Montreal, QC, Canada
Duration: Aug 1 2010Aug 5 2010

Publication series

NameAmerican Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM
NumberPARTS A, B AND C
Volume1
ISSN (Print)0888-8116

Other

OtherASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting, FEDSM 2010 Collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels
CountryCanada
CityMontreal, QC
Period08/1/1008/5/10

ASJC Scopus subject areas

  • Mechanical Engineering

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