Article
Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence
Author/s | Fernández Cara, Enrique
Limaco Ferrel, Juan Dias Bezerra de Menezes, Silvano |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2015-12 |
Deposit Date | 2016-10-20 |
Published in |
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Abstract | This paper deals with the control of a differential turbulence model of the Ladyzhenskaya–Smagorinsky kind. In the equations we find local and nonlocal nonlinearities: the usual transport terms and a turbulent viscosity ... This paper deals with the control of a differential turbulence model of the Ladyzhenskaya–Smagorinsky kind. In the equations we find local and nonlocal nonlinearities: the usual transport terms and a turbulent viscosity that depends on the global in space energy dissipated by the mean flow. We prove that the system is locally null-controllable, with distributed controls locally supported in space. The proof relies on rather well known arguments. However, some specific difficulties are found here because of the occurrence of nonlocal nonlinear terms. We also present an iterative algorithm of the quasi-Newton kind that provides a sequence of states and controls that converge towards a solution to the control problem. Finally, we give the details of a numerical approximation and we illustrate the behavior of the algorithm with a numerical experiment. |
Funding agencies | Dirección General de Enseñanza Superior. España |
Project ID. | MTM2010-15592 |
Citation | Fernández Cara, E., Limaco Ferrel, J. y Dias Bezerra de Menezes, S. (2015). Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence. Journal of Mathematical Fluid Mechanics, 17 (4), 669-698. |
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