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Fluids 2018, 3(4), 84; https://doi.org/10.3390/fluids3040084

Evolve Filter Stabilization Reduced-Order Model for Stochastic Burgers Equation

1
Oak Ridge National Lab, One Bethel Valley Road, Oak Ridge, TN 37831, USA
2
Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL 32306, USA
*
Author to whom correspondence should be addressed.
Received: 6 August 2018 / Revised: 15 September 2018 / Accepted: 18 October 2018 / Published: 26 October 2018
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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Abstract

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results are based on a stochastic Burgers equation with linear multiplicative noise. The numerical result shows that the EF-ROM is significantly better than G-ROM. View Full-Text
Keywords: reduced order modeling; regularization; fluid dynamics; stochastic burgers equation; proper orthogonal decomposition; spatial filter reduced order modeling; regularization; fluid dynamics; stochastic burgers equation; proper orthogonal decomposition; spatial filter
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Xie, X.; Bao, F.; Webster, C.G. Evolve Filter Stabilization Reduced-Order Model for Stochastic Burgers Equation. Fluids 2018, 3, 84.

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