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The effect of uncertain geometries on advection–diffusion of scalar quantitiesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2018 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 58, no 2, p. 509-529Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2018. Vol. 58, no 2, p. 509-529
##### Keywords [en]

Incompressible flow, Advection–diffusion, Uncertainty quantification, Uncertain geometry, Boundary conditions, Parabolic problems, Variable coefficient, Temperature field, Heat transfer
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:liu:diva-140135DOI: 10.1007/s10543-017-0676-7ISI: 000432718100012OAI: oai:DiVA.org:liu-140135DiVA, id: diva2:1137413
#####

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##### Note

##### In thesis

The two dimensional advection–diffusion equation in a stochastically varyinggeometry is considered. The varying domain is transformed into a fixed one andthe numerical solution is computed using a high-order finite difference formulationon summation-by-parts form with weakly imposed boundary conditions. Statistics ofthe solution are computed non-intrusively using quadrature rules given by the probabilitydensity function of the random variable. As a quality control, we prove that thecontinuous problem is strongly well-posed, that the semi-discrete problem is stronglystable and verify the accuracy of the scheme. The technique is applied to a heat transferproblem in incompressible flow. Statistical properties such as confidence intervals andvariance of the solution in terms of two functionals are computed and discussed. Weshow that there is a decreasing sensitivity to geometric uncertainty as we graduallylower the frequency and amplitude of the randomness. The results are less sensitiveto variations in the correlation length of the geometry.

Funding agencies: European Union [ACP3-GA-2013-605036]

Available from: 2017-08-31 Created: 2017-08-31 Last updated: 2018-06-041. Uncertainty quantification for wave propagation and flow problems with random data$(function(){PrimeFaces.cw("OverlayPanel","overlay1196053",{id:"formSmash:j_idt720:0:j_idt724",widgetVar:"overlay1196053",target:"formSmash:j_idt720:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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