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Volume 4, Issue 3-4
An Extended Domain Method for Optimal Boundary Control for Navier-Stokes Equations

Sandro Manservisi

Int. J. Numer. Anal. Mod., 4 (2007), pp. 584-607.

Published online: 2007-04

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  • Abstract

The matching velocity problem for the steady-state Navier-Stokes system is considered. We introduce an extended domain method for solving optimal boundary control problems. The Lagrangian multiplier method is applied to the extended domain with distributed controls and used to determine the optimality system and the control over the boundary of the inner domain. The existence, the differentiability and the optimality system of the control problem are discussed. With this method inflow controls are shown to be numerical reliable over a large admissible control set. Numerical tests for steady-state solutions are presented to prove the effectiveness and robustness of the method for flow matching.

  • Keywords

optimal boundary control, optimal design, Navier-Stokes equations, velocity matching problem.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-584, author = {Manservisi , Sandro}, title = {An Extended Domain Method for Optimal Boundary Control for Navier-Stokes Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {584--607}, abstract = {

The matching velocity problem for the steady-state Navier-Stokes system is considered. We introduce an extended domain method for solving optimal boundary control problems. The Lagrangian multiplier method is applied to the extended domain with distributed controls and used to determine the optimality system and the control over the boundary of the inner domain. The existence, the differentiability and the optimality system of the control problem are discussed. With this method inflow controls are shown to be numerical reliable over a large admissible control set. Numerical tests for steady-state solutions are presented to prove the effectiveness and robustness of the method for flow matching.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/879.html} }
TY - JOUR T1 - An Extended Domain Method for Optimal Boundary Control for Navier-Stokes Equations AU - Manservisi , Sandro JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 584 EP - 607 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/879.html KW - optimal boundary control, optimal design, Navier-Stokes equations, velocity matching problem. AB -

The matching velocity problem for the steady-state Navier-Stokes system is considered. We introduce an extended domain method for solving optimal boundary control problems. The Lagrangian multiplier method is applied to the extended domain with distributed controls and used to determine the optimality system and the control over the boundary of the inner domain. The existence, the differentiability and the optimality system of the control problem are discussed. With this method inflow controls are shown to be numerical reliable over a large admissible control set. Numerical tests for steady-state solutions are presented to prove the effectiveness and robustness of the method for flow matching.

Sandro Manservisi. (1970). An Extended Domain Method for Optimal Boundary Control for Navier-Stokes Equations. International Journal of Numerical Analysis and Modeling. 4 (3-4). 584-607. doi:
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