Commun. Comput. Phys., 5 (2009), pp. 649-666.


Chebyshev Collocation for Optimal Control in a Thermoconvective Flow

M. C. Navarro 1, H. Herrero 1*, S. Hoyas 2

1 Departamento de Matematicas, Facultad de Ciencias Quimicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain.
2 Departamento de Informatica, Escuela de Ingenieria, Universidad de Valencia, 46100 Burjassot, Valencia, Spain.

Received 28 September 2007; Accepted (in revised version) 20 January 2008
Available online 1 August 2008

Abstract

In this paper a Chebyshev collocation method is used for solving numerically an optimal boundary control problem in a thermoconvective fluid flow. The aim of this study is to demonstrate the capabilities of these numerical techniques for handling this kind of problems. As the problem is treated in the primitive variable formulation additional boundary conditions for the pressure and the auxiliary pressure fields are required to avoid spurious modes. A dependence of the convergence of the method on the penalizing parameter that appears in the functional cost is observed. As this parameter approaches zero some singular behaviour in the control function is observed and the order of the method decreases. These singularities are irrelevant in the problem as a regularized control function produces the same results.

AMS subject classifications: 65N35, 76E06, 65K99

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Key words: Chebyshev collocation, optimal boundary control, Boussinesq-Navier-Stokes.

*Corresponding author.
Email: MariaCruz.Navarro@uclm.es (M. C. Navarro), Henar.Herrero@uclm.es (H. Herrero), sergio.hoyas@uv.es (S. Hoyas)
 

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