Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation

I.Y. Gejadze, G.J.M. Copeland, I.M. Navon

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

This paper develops the data-assimilation procedure in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution governed by the free-surface barotropic Navier-Stokes equations. The flow is considered in a 2D vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface. Since a possible application is to the construction of a coastal (limited area) circulation model, the open boundary control problem is the main scope of the paper. The assimilation algorithm is built on the limited memory quasi-Newton LBFGS method guided by the adjoint sensitivities. The analytical step search, which is based on the solution of the tangent linear model, is used. We process the gradients to regularize the solution. In numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements, which could be sufficient for boundary-control identification. As a result of these experiments we formulate some important practical conclusions.
Original languageEnglish
Pages (from-to)1269-1288
Number of pages19
JournalComputers and Mathematics with Applications
Volume52
Issue number8-9
DOIs
Publication statusPublished - 2006

Fingerprint

Data Assimilation
Boundary Control
Boundary Problem
Free Surface
Navier Stokes equations
Control Problem
Navier-Stokes Equations
Limited Memory Method
Vertical
Quasi-Newton Method
Newton-Raphson method
Unsteady Flow
Unsteady flow
Tangent line
Linear Model
Horizontal
Experiments
Numerical Experiment
Sufficient
Gradient

Keywords

  • navier-stokes equations
  • adjoint equations
  • data assimilation
  • cceans
  • waves
  • mathematics

Cite this

Gejadze, I.Y. ; Copeland, G.J.M. ; Navon, I.M. / Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. In: Computers and Mathematics with Applications. 2006 ; Vol. 52, No. 8-9. pp. 1269-1288.
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Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. / Gejadze, I.Y.; Copeland, G.J.M.; Navon, I.M.

In: Computers and Mathematics with Applications, Vol. 52, No. 8-9, 2006, p. 1269-1288.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation

AU - Gejadze, I.Y.

AU - Copeland, G.J.M.

AU - Navon, I.M.

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N2 - This paper develops the data-assimilation procedure in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution governed by the free-surface barotropic Navier-Stokes equations. The flow is considered in a 2D vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface. Since a possible application is to the construction of a coastal (limited area) circulation model, the open boundary control problem is the main scope of the paper. The assimilation algorithm is built on the limited memory quasi-Newton LBFGS method guided by the adjoint sensitivities. The analytical step search, which is based on the solution of the tangent linear model, is used. We process the gradients to regularize the solution. In numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements, which could be sufficient for boundary-control identification. As a result of these experiments we formulate some important practical conclusions.

AB - This paper develops the data-assimilation procedure in order to allow for the assimilation of measurements of currents and free-surface elevations into an unsteady flow solution governed by the free-surface barotropic Navier-Stokes equations. The flow is considered in a 2D vertical section in which horizontal and vertical components of velocity are represented as well as the elevation of the free surface. Since a possible application is to the construction of a coastal (limited area) circulation model, the open boundary control problem is the main scope of the paper. The assimilation algorithm is built on the limited memory quasi-Newton LBFGS method guided by the adjoint sensitivities. The analytical step search, which is based on the solution of the tangent linear model, is used. We process the gradients to regularize the solution. In numerical experiments we consider different wave patterns with a purpose to specify a set of incomplete measurements, which could be sufficient for boundary-control identification. As a result of these experiments we formulate some important practical conclusions.

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KW - cceans

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