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Article: Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows

TitleError estimates for a POD method for solving viscous G-equations in incompressible cellular flows
Authors
Issue Date2021
PublisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/SIAM-journal-on-scientific-computing-sisc
Citation
SIAM Journal on Scientific Computing, 2021, v. 43 n. 1, p. A636-A662 How to Cite?
AbstractThe G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing regular solutions of viscous G-equations in incompressible steady and time-periodic cellular flows. Our method is based on the Galerkin proper orthogonal decomposition (POD) method. To facilitate the algorithm design and convergence analysis, we decompose the solution of the viscous G-equation into a mean-free part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the mean-free part. With the POD basis, we can efficiently solve the evolution equation for the mean-free part of the solution to the viscous G-equation. After we get the mean-free part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for viscous G-equations and curvature G-equations are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows.
Persistent Identifierhttp://hdl.handle.net/10722/294085
ISSN
2023 Impact Factor: 3.0
2023 SCImago Journal Rankings: 1.803
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorGu, H-
dc.contributor.authorXin, J-
dc.contributor.authorZhang, Z-
dc.date.accessioned2020-11-23T08:26:07Z-
dc.date.available2020-11-23T08:26:07Z-
dc.date.issued2021-
dc.identifier.citationSIAM Journal on Scientific Computing, 2021, v. 43 n. 1, p. A636-A662-
dc.identifier.issn1064-8275-
dc.identifier.urihttp://hdl.handle.net/10722/294085-
dc.description.abstractThe G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing regular solutions of viscous G-equations in incompressible steady and time-periodic cellular flows. Our method is based on the Galerkin proper orthogonal decomposition (POD) method. To facilitate the algorithm design and convergence analysis, we decompose the solution of the viscous G-equation into a mean-free part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the mean-free part. With the POD basis, we can efficiently solve the evolution equation for the mean-free part of the solution to the viscous G-equation. After we get the mean-free part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for viscous G-equations and curvature G-equations are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows.-
dc.languageeng-
dc.publisherSociety for Industrial and Applied Mathematics. The Journal's web site is located at https://www.siam.org/Publications/Journals/SIAM-journal-on-scientific-computing-sisc-
dc.relation.ispartofSIAM Journal on Scientific Computing-
dc.rights© [year] Society for Industrial and Applied Mathematics. First Published in [Publication] in [volume and number, or year], published by the Society for Industrial and Applied Mathematics (SIAM).-
dc.titleError estimates for a POD method for solving viscous G-equations in incompressible cellular flows-
dc.typeArticle-
dc.identifier.emailZhang, Z: zhangzw@hku.hk-
dc.identifier.authorityZhang, Z=rp02087-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/19M1241854-
dc.identifier.scopuseid_2-s2.0-85109513805-
dc.identifier.hkuros319604-
dc.identifier.volume43-
dc.identifier.issue1-
dc.identifier.spageA636-
dc.identifier.epageA662-
dc.identifier.isiWOS:000623833100002-
dc.publisher.placeUnited States-
dc.identifier.issnl1064-8275-

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