Two-parameter extremum problems of boundary control for stationary thermal convection equations

Two-parameter extremum problems of boundary control are formulated for the stationary thermal convection equations with Dirichlet boundary conditions for velocity and with mixed boundary conditions for temperature. The cost functional is defined as the root mean square integral deviation of the desi...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2011-09, Vol.51 (9), p.1539-1557
Main Authors: Alekseev, G. V., Tereshko, D. A.
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Computational mathematics
Computational Mathematics and Numerical Analysis
Fluid dynamics
Heat
Heat conductivity
Mathematical analysis
Mathematics
Mathematics and Statistics
Studies
Temperature
Velocity
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Summary:Two-parameter extremum problems of boundary control are formulated for the stationary thermal convection equations with Dirichlet boundary conditions for velocity and with mixed boundary conditions for temperature. The cost functional is defined as the root mean square integral deviation of the desired velocity (vorticity, or pressure) field from one given in some part of the flow region. Controls are the boundary functions involved in the Dirichlet condition for velocity on the boundary of the flow region and in the Neumann condition for temperature on part of the boundary. The uniqueness of the extremum problems is analyzed, and the stability of solutions with respect to certain perturbations in the cost functional and one of the functional parameters of the original model is estimated. Numerical results for a control problem associated with the minimization of the vorticity norm aimed at drag reduction are discussed.
ISSN:0965-5425
1555-6662
DOI:10.1134/S096554251109003X