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Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials

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Abstract

We consider in this paper numerical approximations of the immiscible binary mixture of nematic liquid crystals (LCs) and viscous fluids. We develop a second-order time marching scheme by adopting the recently developed stabilized-SAV (scalar auxiliary variable) approach where several critical stabilization terms are added to enhance the stability; thus, large time steps are allowed in computations. The scheme is highly efficient and one only needs to solve several decoupled linear equations with constant coefficients at each time step. The energy stability of the scheme is proved, and various 2D and 3D numerical experiments including the drop deformations and phase separations are then performed to validate the accuracy and energy stability of the proposed scheme.

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Funding

Y. Sui is partially supported by Humanities and Social Science Research Projects of Ministry of Education of the People’s Republic of China (No.18YJC790142). G. Jin is partially supported by National Natural Science Foundation of China (No.71862034).

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Authors and Affiliations

  1. College of Economics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Yubing Sui

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Jingzhou Jiang

  3. School of Logistics, Yunnan University of Finance and Economics, Kunming, China

    Guigen Jin

  4. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Xiaofeng Yang

Authors
  1. Yubing Sui
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  2. Jingzhou Jiang
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  3. Guigen Jin
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  4. Xiaofeng Yang
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Corresponding authors

Correspondence to Guigen Jin or Xiaofeng Yang.

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Communicated by: Carlos Garcia-Cervera

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Sui, Y., Jiang, J., Jin, G. et al. Second-order accurate and energy stable numerical scheme for an immiscible binary mixture of nematic liquid crystals and viscous fluids with strong anchoring potentials. Adv Comput Math 47, 38 (2021). https://doi.org/10.1007/s10444-021-09865-8

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  • DOI: https://doi.org/10.1007/s10444-021-09865-8

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