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Volume 15, Issue 4-5
Regularized Reduced Order Models for a Stochastic Burgers Equation

T. Iliescu, Honghu Liu & Xuping Xie

Int. J. Numer. Anal. Mod., 15 (2018), pp. 594-607.

Published online: 2018-04

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  • 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.

  • Keywords

Reduced order modeling, Leray regularized model, stabilization method, numerical instability, stochastic Burgers equation, differential filter.

  • AMS Subject Headings

34F05, 35R60, 37L55, 60H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

iliescu@vt.edu (T. Iliescu)

hhliu@vt.edu (Honghu Liu)

xupingxy@vt.edu (Xuping Xie)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-594, author = {Iliescu , T.Liu , Honghu and Xie , Xuping}, title = {Regularized Reduced Order Models for a Stochastic Burgers Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {4-5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12533.html} }
TY - JOUR T1 - Regularized Reduced Order Models for a Stochastic Burgers Equation AU - Iliescu , T. AU - Liu , Honghu AU - Xie , Xuping JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 594 EP - 607 PY - 2018 DA - 2018/04 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12533.html KW - Reduced order modeling, Leray regularized model, stabilization method, numerical instability, stochastic Burgers equation, differential filter. AB -

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.

Iliescu , T.Liu , Honghu and Xie , Xuping. (2018). Regularized Reduced Order Models for a Stochastic Burgers Equation. International Journal of Numerical Analysis and Modeling. 15 (4-5). 594-607. doi:
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