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An overview on numerical analyses of nematic liquid crystal flows

Opened Access An overview on numerical analyses of nematic liquid crystal flows

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Autor: Badia Rodríguez, Santiago
Guillén González, Francisco Manuel
Gutiérrez Santacreu, Juan Vicente
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2011-09
Publicado en: Archives of Computational Methods in Engineering, 18, 285-313.
Tipo de documento: Artículo
Resumen: The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern the motion of a nematic liquid crystal. This system, in its simplest form, consists of the Navier-Stokes equations coupled with an extra anisotropic stress tensor, which represents the effect of the nematic liquid crystal on the fluid, and a convective harmonic map equation. The sphere constraint must be enforced almost everywhere in order to obtain an energy estimate. Since an almost everywhere satisfaction of this restriction is not appropriate at a numerical level, two alternative approaches have been introduced: a penalty method and a saddle-point method. These approaches are suitable for their numerical approximation by finite elements, since a discrete version of the restriction is enough to prove the desired energy estimate. The Ginzburg-Landau penalty function is usually used to enforce the sphere constrain...
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Cita: Badia Rodríguez, S., Guillén González, F.M. y Gutiérrez Santacreu, J.V. (2011). An overview on numerical analyses of nematic liquid crystal flows. Archives of Computational Methods in Engineering, 18, 285-313.
Tamaño: 531.4Kb
Formato: PDF

URI: http://hdl.handle.net/11441/47880

DOI: 10.1007/s11831-011-9061-x

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