Year: 2018
Author: T. Iliescu, Honghu Liu, Xuping Xie
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 594–607
Abstract
In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results suggest that, in a convection-dominated regime, standard reduced order models yield inaccurate results in the form of spurious numerical oscillations. To alleviate these oscillations, we use the Leray reduced order model, which increases the numerical stability of the standard model by smoothing (regularizing) the convective term with an explicit spatial filter. The Leray reduced order model yields significantly better results than the standard reduced order model and is more robust with respect to changes in the strength of the noise.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12533
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 594–607
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Reduced order modeling Leray regularized model stabilization method numerical instability stochastic Burgers equation differential filter.