Continuous Data Assimilation Applied To A Velocity-Vorticity Formulation Of The 2d Navier-Stokes Equations

Matthew Gardner; Adam Larios; Leo G. Rebholz; Duygu Vargun; Camille Zerfas

doi:10.3934/era.2020113

Continuous Data Assimilation Applied To A Velocity-Vorticity Formulation Of The 2d Navier-Stokes Equations

Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun, Camille Zerfas

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the ve-locity only. We prove that under a typical ﬁnite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is ap-plied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its electiveness on an application problem of channel ﬂow past a ﬂat plate.

Original language	English
Pages (from-to)	2223-2247
Number of pages	25
Journal	Electronic Research Archive
Volume	29
Issue number	3
DOIs	https://doi.org/10.3934/era.2020113
State	Published - Aug 2021

Funding

2020 Mathematics Subject Classification. Primary: 65M60; Secondary: 76D05. Key words and phrases. Data assimilation, Navier-Stokes equations, velocity-vorticity scheme. The second author is supported by NSF Grants DMS 1716801 and CMMI 1953346. The third and fourth authors are supported by NSF Grant DMS 2011490.

Keywords

Data assimilation
Navier-Stokes equations
velocity-vorticity scheme.

Access to Document

10.3934/era.2020113

Cite this

@article{58d7764e0b6645598d276e95a3d2c059,

title = "Continuous Data Assimilation Applied To A Velocity-Vorticity Formulation Of The 2d Navier-Stokes Equations",

abstract = "We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the ve-locity only. We prove that under a typical ﬁnite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is ap-plied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its electiveness on an application problem of channel ﬂow past a ﬂat plate.",

keywords = "Data assimilation, Navier-Stokes equations, velocity-vorticity scheme.",

author = "Matthew Gardner and Adam Larios and Rebholz, \{Leo G.\} and Duygu Vargun and Camille Zerfas",

year = "2021",

month = aug,

doi = "10.3934/era.2020113",

language = "English",

volume = "29",

pages = "2223--2247",

journal = "Electronic Research Archive",

issn = "2688-1594",

publisher = "American Institute of Mathematical Sciences (AIMS)",

number = "3",

}

TY - JOUR

T1 - Continuous Data Assimilation Applied To A Velocity-Vorticity Formulation Of The 2d Navier-Stokes Equations

AU - Gardner, Matthew

AU - Larios, Adam

AU - Rebholz, Leo G.

AU - Vargun, Duygu

AU - Zerfas, Camille

PY - 2021/8

Y1 - 2021/8

N2 - We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the ve-locity only. We prove that under a typical ﬁnite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is ap-plied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its electiveness on an application problem of channel ﬂow past a ﬂat plate.

AB - We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the ve-locity only. We prove that under a typical ﬁnite element spatial discretization and backward Euler temporal discretization, application of CDA preserves the unconditional long-time stability property of the velocity-vorticity method and provides optimal long-time accuracy. These properties hold if nudging is ap-plied only to the velocity, and if nudging is also applied to the vorticity then the optimal long-time accuracy is achieved more rapidly in time. Numerical tests illustrate the theory, and show its electiveness on an application problem of channel ﬂow past a ﬂat plate.

KW - Data assimilation

KW - Navier-Stokes equations

KW - velocity-vorticity scheme.

UR - https://www.scopus.com/pages/publications/85113638831

U2 - 10.3934/era.2020113

DO - 10.3934/era.2020113

M3 - Article

AN - SCOPUS:85113638831

SN - 2688-1594

VL - 29

SP - 2223

EP - 2247

JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 3

ER -

Continuous Data Assimilation Applied To A Velocity-Vorticity Formulation Of The 2d Navier-Stokes Equations

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this