Opened Access Approximation of Smectic-A liquid crystals

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Autor: Guillén González, Francisco Manuel
Tierra Chica, Giordano
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2015-06-15
Publicado en: Computer Methods in Applied Mechanics and Engineering, 290, 342-361.
Tipo de documento: Artículo
Resumen: In this paper, we present energy-stable numerical schemes for a Smectic-A liquid crystal model. This model involve the hydrodynamic velocity-pressure macroscopic variables (u, p) and the microscopic order parameter of Smectic-A liquid crystals, where its molecules have a uniaxial orientational order and a positional order by layers of normal and unitary vector n. We start from the formulation given in [E’97] by using the so-called layer variable φ such that n = ∇φ and the level sets of φ describe the layer structure of the Smectic-A liquid crystal. Then, a strongly non-linear parabolic system is derived coupling velocity and pressure unknowns of the Navier-Stokes equations (u, p) with a fourth order parabolic equation for φ. We will give a reformulation as a mixed second order problem which let us to define some new energy-stable numerical schemes, by using second order finite differences in time and C 0 - finite elements in space. Finally, numerical simulations are presen...
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Cita: Guillén González, F.M. y Tierra Chica, G. (2015). Approximation of Smectic-A liquid crystals. Computer Methods in Applied Mechanics and Engineering, 290, 342-361.
Tamaño: 1.200Mb
Formato: PDF

URI: http://hdl.handle.net/11441/42929

DOI: http://dx.doi.org/10.1016/j.cma.2015.03.015

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