Numerical Approximations for a Smectic-A Liquid Crystal Flow Model: First-Order, Linear, Decoupled and Energy Stable Schemes
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.
Q. Huang et al., "Numerical Approximations for a Smectic-A Liquid Crystal Flow Model: First-Order, Linear, Decoupled and Energy Stable Schemes," Discrete and Continuous Dynamical Systems - Series B, vol. 23, no. 6, pp. 2193-2216, American Institute of Mathematical Sciences, Aug 2018.
The definitive version is available at https://doi.org/10.3934/dcdsb.2018230
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Cahn-Hilliard equation; Energy stable
International Standard Serial Number (ISSN)
Article - Journal
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01 Aug 2018