A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tome and McKee [32]; Tome et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution. (C) 2009 Elsevier B.V. All rights reserved.FAPESP - Fundacao de Amparo a pesquisa do Estado de Sao Paulo[04/16064-9]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP - Fundacao de Amparo a pesquisa do Estado de Sao Paulo[07/07038-2]CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[304422/2007-0]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico[470764/20074]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq