Finite element approximation of nematic liquid crystal flows using a saddle-point structure
Finite element approximation of nematic liquid crystal flows using a saddle-point structure
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DOI：
10.1016/j.jcp.2010.11.033
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发表时间：
2011-02-20
影响因子：
4.1
通讯作者：
Vicente Gutierrez-Santacreu, Juan
中科院分区：
文献类型：
--
作者：
Badia, Santiago;Guillen-Gonzalez, Francisco;Vicente Gutierrez-Santacreu, Juan
In this work, we propose finite element schemes for the numerical approximation of nematic liquid crystal flows, based on a saddle-point formulation of the director vector subproblem. It introduces a Lagrange multiplier that allows to enforce the sphere condition. In this setting, we can consider the limit problem (without penalty) and the penalized problem (using a Ginzburg-Landau penalty function) in a unified way. Further, the resulting schemes have a stable behavior with respect to the value of the penalty parameter, a key difference with respect to the existing schemes. Two different methods have been considered for the time integration. First, we have considered an implicit algorithm that is unconditionally stable and energy preserving. The linearization of the problem at every time step value can be performed using a quasi-Newton method that allows to decouple fluid velocity and director vector computations for every tangent problem. Then, we have designed a linear semi-implicit algorithm (i.e. it does not involve nonlinear iterations) ant proved that it is unconditionally stable, verifying a discrete energy inequality. Finally, SOME numerical simulations are provided. (C) 2010 Elsevier Inc. All rights reserved
