## A Decoupled and Energy Stable Scheme for Smectic-A Liquid Crystal Flows

- April 20, 2016
- 1:15 p.m.
- LeConte 312

## Abstract

In this talk, we consider the numerical approximations for the smectic-A liquid crystal model. The model equation, that is derived from the variational approach of the de-Gennes energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations, and two nonlinear coupled second-order elliptic equations. Based on some subtle explicit (implicit treatments for nonlinear terms), we develop a 1st order, unconditionally energy stable, linear, decoupled time discretization scheme. Stability analysis and ample numerical simulations are presented thereafter. We also rigorously prove that that the proposed scheme obeys the energy dissipation law. Various numerical simulations are presented to demonstrate accuracy and stability thereafter.