Title: Uncertainty quantification for thermo-convective Poiseuille flow using stochastic collocation

Authors: Bettina Schieche; Jens Lang

Addresses: Graduate School of Computational Engineering, Center of Smart Interfaces, Numerical Analysis and Scientific Computing, Department of Mathematics, Technische Universität Darmstadt, Dolivostrasse 15, 64293 Darmstadt, Germany ' Graduate School of Computational Engineering, Center of Smart Interfaces, Numerical Analysis and Scientific Computing, Department of Mathematics, Technische Universität Darmstadt, Dolivostrasse 15, 64293 Darmstadt, Germany

Abstract: Simulations become more reliable if they include random effects. One way to express uncertainties in the describing parameters are correlated random fields. Typically, the resulting problem is a partial differential equation (PDE) with random parameters. These additional, stochastic dimensions can be discretised either by spectral methods or stochastic collocation. The aim of this work is to analyse effects of an uncertain heating condition for plane Poiseuille flow by means of an adaptive, anisotropic stochastic collocation method. Additionally, we are interested in how the heat exchange can be improved by small surface variations. We show that the fluctuations of the resulting flow continuously depend on the input fluctuations. Furthermore, we can find specific surface structures that improve the heat exchange.

Keywords: computational engineering; Navier-Stokes; Boussinesq approximation; thermal coupling; Poiseuille flow; heat exchange; Nusselt number; surface variations; uncertainty quantification; PDEs; partial differential equations; random parameters; stochastic collocation; sparse grids; adaptivity; heat transfer; simulation.

DOI: 10.1504/IJCSE.2014.064532

International Journal of Computational Science and Engineering, 2014 Vol.9 No.5/6, pp.465 - 477

Received: 28 Oct 2011
Accepted: 22 Aug 2012

Published online: 22 Sep 2014 *

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