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

Cruz, P.A. and Tome, M.F. and Stewart, I.W. and McKee, S. (2010) A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. Journal of Non-Newtonian Fluid Mechanics, 165 (3-4). pp. 143-157. ISSN 0377-0257

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Abstract

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 (Tomé and McKee [32]; Tomé 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.