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 - <p style="text-align: justify;">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.</p>