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Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows

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Abstract

In this paper, we develop a first-order and a second-order coupled energy stable numerical scheme respectively for a Q-tensor based hydrodynamic model of nematic liquid crystal flows. We then extend the first order coupled scheme to a decoupled scheme and show that it is energy stable as well. The fully coupled schemes are implemented in 2-dimensional space and time, with which we study defect dynamics in flows of nematic liquid crystals in a channel. The numerical schemes are shown to be efficient in solving the Q-tensor based liquid crystal model. The methodology developed here also provides a paradigm for developing energy-stable schemes for more general hydrodynamic models of complex fluids which obey an energy dissipation law.

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Acknowledgments

Jia Zhao and Qi Wang are partially supported by NSF-DMS-1200487 and NSF-DMS-1517347, NIH-2R01GM078994-05A1, AFOSR-FA9550-12-1-0178, and an SC EPSCOR/IDEA award. In addition, Jia Zhao is also supported by a Dissertation Fellowship from the Provost Office of USC.

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Authors and Affiliations

  1. Department of Mathematics, Interdisciplinary Mathematics Institute and NanoCenter at USC, University of South Carolina, Columbia, SC, 29208, USA

    Jia Zhao & Qi Wang

  2. Beijing Computational Science Research Center, Beijing, 100193, China

    Qi Wang

  3. School of Mathematics, Nankai University, Tianjin, 300071, China

    Qi Wang

Authors
  1. Jia Zhao
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  2. Qi Wang
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Correspondence to Qi Wang.

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Zhao, J., Wang, Q. Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows. J Sci Comput 68, 1241–1266 (2016). https://doi.org/10.1007/s10915-016-0177-x

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  • DOI: https://doi.org/10.1007/s10915-016-0177-x

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