Numerical Approximations for a Smectic-A Liquid Crystal Flow Model: First-Order, Linear, Decoupled and Energy Stable Schemes

Abstract

In this paper, we consider numerical approximations for a model of smectic-A liquid crystal flows in its weak flow limit. The model, derived from the variational approach of the de Gennes free energy, is consisted of a highly nonlinear system that couples the incompressible Navier-Stokes equations with two nonlinear order parameter equations. Based on some subtle explicit—implicit treatments for nonlinear terms, we develop an unconditionally energy stable, linear and decoupled time marching numerical scheme for the reduced model in the weak flow limit. We also rigorously prove that the numerical scheme obeys the energy dissipation law at the discrete level. Various numerical simulations are presented to demonstrate the accuracy and the stability of the scheme.

Department(s)

Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Cahn-Hilliard equation; Energy stable

International Standard Serial Number (ISSN)

1531-3492; 1553-524X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Aug 2018

Link to Full Text

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