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Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence

Opened Access Theoretical and numerical local null controllability of a Ladyzhenskaya-Smagorinsky model of turbulence

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Autor: Fernández Cara, Enrique
Limaco Ferrel, Juan
Dias Bezerra de Menezes, Silvano
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2015-12
Publicado en: Journal of Mathematical Fluid Mechanics, 17 (4), 669-698.
Tipo de documento: Artículo
Resumen: 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.
Cita: 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.
Tamaño: 1.488Mb
Formato: PDF

URI: http://hdl.handle.net/11441/47795

DOI: 10.1007/s00021-015-0232-7

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