Downscaling the 2D Bénard convection equations using continuous data assimilation

Handle URI:
http://hdl.handle.net/10754/623051
Title:
Downscaling the 2D Bénard convection equations using continuous data assimilation
Authors:
Altaf, Muhammad; Titi, E. S.; Gebrael, T.; Knio, Omar; Zhao, L.; McCabe, Matthew ( 0000-0002-1279-5272 ) ; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
We consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Bénard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit between some interpolants of the assimilated coarse-grid measurements and the fine-grid model solution, is added to the model equations to constrain the model. The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity. These measurements are assimilated either separately or simultaneously, and the results are compared against those resulting from the standard point-to-point nudging approach (NA). Our numerical results suggest that the CDA solution outperforms that of NA, always converging to the true solution when the velocity is assimilated as has been theoretically proven. Assimilation of temperature measurements only may not always recover the true state as demonstrated in the case study. Various runs are conducted to evaluate the sensitivity of CDA to noise in the measurements, the size, and the time frequency of the measured grid, suggesting a more robust behavior of CDA compared to that of NA.
KAUST Department:
Water Desalination and Reuse Research Center (WDRC); Biological and Environmental Sciences and Engineering (BESE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Environmental Science and Engineering Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program
Citation:
Altaf MU, Titi ES, Gebrael T, Knio OM, Zhao L, et al. (2017) Downscaling the 2D Bénard convection equations using continuous data assimilation. Computational Geosciences. Available: http://dx.doi.org/10.1007/s10596-017-9619-2.
Publisher:
Springer Nature
Journal:
Computational Geosciences
Issue Date:
27-Feb-2017
DOI:
10.1007/s10596-017-9619-2
Type:
Article
ISSN:
1420-0597; 1573-1499
Sponsors:
The work of E.S.Titi was supported in part by the ONR grant N00014-15-1-2333 and the NSF grants DMS-1109640 and DMS-1109645.
Additional Links:
http://link.springer.com/article/10.1007/s10596-017-9619-2
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Water Desalination and Reuse Research Center (WDRC); Biological and Environmental Sciences and Engineering (BESE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAltaf, Muhammaden
dc.contributor.authorTiti, E. S.en
dc.contributor.authorGebrael, T.en
dc.contributor.authorKnio, Omaren
dc.contributor.authorZhao, L.en
dc.contributor.authorMcCabe, Matthewen
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2017-03-20T12:44:54Z-
dc.date.available2017-03-20T12:44:54Z-
dc.date.issued2017-02-27en
dc.identifier.citationAltaf MU, Titi ES, Gebrael T, Knio OM, Zhao L, et al. (2017) Downscaling the 2D Bénard convection equations using continuous data assimilation. Computational Geosciences. Available: http://dx.doi.org/10.1007/s10596-017-9619-2.en
dc.identifier.issn1420-0597en
dc.identifier.issn1573-1499en
dc.identifier.doi10.1007/s10596-017-9619-2en
dc.identifier.urihttp://hdl.handle.net/10754/623051-
dc.description.abstractWe consider a recently introduced continuous data assimilation (CDA) approach for downscaling a coarse resolution configuration of the 2D Bénard convection equations into a finer grid. In this CDA, a nudging term, estimated as the misfit between some interpolants of the assimilated coarse-grid measurements and the fine-grid model solution, is added to the model equations to constrain the model. The main contribution of this study is a performance analysis of CDA for downscaling measurements of temperature and velocity. These measurements are assimilated either separately or simultaneously, and the results are compared against those resulting from the standard point-to-point nudging approach (NA). Our numerical results suggest that the CDA solution outperforms that of NA, always converging to the true solution when the velocity is assimilated as has been theoretically proven. Assimilation of temperature measurements only may not always recover the true state as demonstrated in the case study. Various runs are conducted to evaluate the sensitivity of CDA to noise in the measurements, the size, and the time frequency of the measured grid, suggesting a more robust behavior of CDA compared to that of NA.en
dc.description.sponsorshipThe work of E.S.Titi was supported in part by the ONR grant N00014-15-1-2333 and the NSF grants DMS-1109640 and DMS-1109645.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s10596-017-9619-2en
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s10596-017-9619-2en
dc.subjectContinuous data assimilationen
dc.subjectBénard convection equationsen
dc.subjectDynamical downscalingen
dc.titleDownscaling the 2D Bénard convection equations using continuous data assimilationen
dc.typeArticleen
dc.contributor.departmentWater Desalination and Reuse Research Center (WDRC)en
dc.contributor.departmentBiological and Environmental Sciences and Engineering (BESE) Divisionen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalComputational Geosciencesen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, USAen
dc.contributor.institutionAmerican University of Beirut, Beirut, Lebanonen
dc.contributor.institutionGeorgia Institute of Technology, Atlanta, USAen
kaust.authorAltaf, Muhammaden
kaust.authorKnio, Omaren
kaust.authorMcCabe, Matthewen
kaust.authorHoteit, Ibrahimen
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