TY - JOUR
T1 - A Three-Stage Operator-Splitting/Finite Element Method for the Numerical Simulation of Liquid Crystal Flow
AU - Glowinski , R.
AU - Lin , P.
AU - Pan , X.-B.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 440
EP - 454
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/777.html
KW - liquid crystal, incompressible flow, finite element method, operator-splitting method.
AB - <p style="text-align: justify;">In this article, we investigate the application of an operator-splitting/finite element method to the numerical simulation of a liquid crystal &nbsp;flow. The operator-splitting is achieved through three stages, so that each
stage is simpler and easier to deal with than the step of any un-split implicit
scheme. The first stage deals with the system coupling a Stokes equation for
velocity with an equation modeling the diffusion of the liquid crystal director field. The second stage deals with the convection of both the velocity and director field; a wave-like equation approach is used to treat this advection part
and proves being quite efficient. Finally, the third stage deals with the nonlinear terms; a (quasi) closed form solution can be derived for this stage. Overall,
with this type of splitting, the nonlinear terms in the liquid crystal model can
be treated quite easily. The results of several numerical experiments show the
good performances of the three-stage splitting method discussed in this article.</p>