期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 227, 期 2, 页码 1411-1427出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2007.09.005
关键词
liquid crystal flow; non-newtonian fluids; C-0 finite element approximation; discrete energy law; singularity dynamics
In this paper, we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain Q. We reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in W1.2+sigma(Omega) (sigma > 0 is an arbitrarily small number). This enables us to use convenient conformal C-0 finite elements in solving the problem. Moreover, a discrete energy law is derived for a modified midpoint time discretization scheme. A fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately. A number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method. (c) 2007 Elsevier Inc. All rights reserved.
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