Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model

Handle URI:
http://hdl.handle.net/10754/621387
Title:
Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model
Authors:
Markowich, Peter A. ( 0000-0002-3704-1821 ) ; Titi, Edriss S; Trabelsi, Saber
Abstract:
In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtain improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present a few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the convergence analysis of the data assimilation algorithm. © 2016 IOP Publishing Ltd & London Mathematical Society.
KAUST Department:
Division of Math and Computer Sci. and Eng., King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Citation:
Markowich PA, Titi ES, Trabelsi S (2016) Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model. Nonlinearity 29: 1292–1328. Available: http://dx.doi.org/10.1088/0951-7715/29/4/1292.
Publisher:
IOP Publishing
Journal:
Nonlinearity
Issue Date:
9-Mar-2016
DOI:
10.1088/0951-7715/29/4/1292
Type:
Article
ISSN:
0951-7715; 1361-6544
Sponsors:
EST is thankful to the kind hospitality of KAUST where this work was started. EST also acknowledges the partial support of the National Science Foundation through grants number DMS-1109640 and DMS-1109645. The research of P A Markowich and S Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorMarkowich, Peter A.en
dc.contributor.authorTiti, Edriss Sen
dc.contributor.authorTrabelsi, Saberen
dc.date.accessioned2016-11-03T08:28:07Z-
dc.date.available2016-11-03T08:28:07Z-
dc.date.issued2016-03-09en
dc.identifier.citationMarkowich PA, Titi ES, Trabelsi S (2016) Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model. Nonlinearity 29: 1292–1328. Available: http://dx.doi.org/10.1088/0951-7715/29/4/1292.en
dc.identifier.issn0951-7715en
dc.identifier.issn1361-6544en
dc.identifier.doi10.1088/0951-7715/29/4/1292en
dc.identifier.urihttp://hdl.handle.net/10754/621387-
dc.description.abstractIn this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtain improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present a few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the convergence analysis of the data assimilation algorithm. © 2016 IOP Publishing Ltd & London Mathematical Society.en
dc.description.sponsorshipEST is thankful to the kind hospitality of KAUST where this work was started. EST also acknowledges the partial support of the National Science Foundation through grants number DMS-1109640 and DMS-1109645. The research of P A Markowich and S Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.en
dc.publisherIOP Publishingen
dc.subjectBrinkman-Forchheimer-extended Darcy modelen
dc.subjectdata assimilationen
dc.subjectdown-scalingen
dc.titleContinuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy modelen
dc.typeArticleen
dc.contributor.departmentDivision of Math and Computer Sci. and Eng., King Abdullah University of Science and Technology, Thuwal, Saudi Arabiaen
dc.identifier.journalNonlinearityen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, 3368-TAMU, College Station, TX, United Statesen
kaust.authorMarkowich, Peter A.en
kaust.authorTrabelsi, Saberen
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