### Abstract

Original language | English |
---|---|

Pages (from-to) | 1269-1288 |

Number of pages | 19 |

Journal | Computers and Mathematics with Applications |

Volume | 52 |

Issue number | 8-9 |

DOIs | |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

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

### Cite this

*Computers and Mathematics with Applications*,

*52*(8-9), 1269-1288. https://doi.org/10.1016/j.camwa.2006.11.005

}

*Computers and Mathematics with Applications*, vol. 52, no. 8-9, pp. 1269-1288. https://doi.org/10.1016/j.camwa.2006.11.005

**Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation.** / Gejadze, I.Y.; Copeland, G.J.M.; Navon, I.M.

Research output: Contribution to journal › Article

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.

PY - 2006

Y1 - 2006

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.

KW - navier-stokes equations

KW - adjoint equations

KW - data assimilation

KW - cceans

KW - waves

KW - mathematics

UR - http://dx.doi.org/10.1016/j.camwa.2006.11.005

U2 - 10.1016/j.camwa.2006.11.005

DO - 10.1016/j.camwa.2006.11.005

M3 - Article

VL - 52

SP - 1269

EP - 1288

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 8-9

ER -