Finite element approximation of nematic liquid crystal flows using a saddle-point structure

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Badia, Santiago¹  Guillen-Gonzalez, Francisco²  Vicente Gutierrez-Santacreu, Juan³ 

[1] Univ Politecn Cataluna, Int Ctr Numer Methods Engn CIMNE, Barcelona 08034, Spain

[2] Univ Seville, Dpto Ecuaciones Diferenciales & Anal Numer, Seville 41012, Spain

[3] Univ Seville, Dpto Matemat Aplicada 1, Seville 41012, Spain

关键词: Nematic liquid crystals;    Finite element methods;    Saddle-point problems;    Ericksen-Leslie problem;    Ginzburg-Landau problem;   

DOI  :  10.1016/j.jcp.2010.11.033

来源: Elsevier

【 摘 要 】

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

【 授权许可】

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