A numerical method for solving the dynamic three-dimensional Ericksen–Leslie equations for nematic liquid crystals subject to a strong magnetic field |
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Authors: | Pedro A Cruz Murilo F Tomé Iain W Stewart Sean McKee |
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Institution: | 1. Helmut Schmidt University, Institute of Mechanics, Hamburg D-22039, Germany;2. IAV GmbH, Entwicklungszentrum, Berlin D-10587, Germany |
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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. |
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