### Abstract

Original language | English |
---|---|

Pages (from-to) | 109-136 |

Number of pages | 28 |

Journal | Journal of Computational Physics |

Volume | 247 |

DOIs | |

Publication status | Published - 15 Aug 2013 |

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### Keywords

- two-dimensional flow
- Ericksen-Leslie equations
- nematic liquid crystal
- analytic solution
- finite difference

### Cite this

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*Journal of Computational Physics*, vol. 247, pp. 109-136. https://doi.org/10.1016/j.jcp.2013.03.061

**Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows.** / Cruz, P.A.; Tome, Murilo F.; Stewart, Iain W.; McKee, Sean.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows

AU - Cruz, P.A.

AU - Tome, Murilo F.

AU - Stewart, Iain W.

AU - McKee, Sean

PY - 2013/8/15

Y1 - 2013/8/15

N2 - A finite difference method for solving nematic liquid crystal flows under the effect of a magnetic field is developed. The dynamic equations of nematic liquid crystals, given by the Ericksen–Leslie dynamic theory, are employed. These are expressed in terms of primitive variables and solved employing the ideas behind the GENSMAC methodology (Tomé and McKee, 1994; Tomé et al., 2002) [38,41]. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. By employing fully developed flow assumptions an analytic solution for steady 2D-channel flow is found. The resulting numerical technique was then, in part, validated by comparing numerical solutions against this analytic solution. Convergence results are presented. To demonstrate the capabilities of the numerical method, the flow of a nematic liquid crystal through various complex geometries are then simulated. Results are obtained for L-shaped channels and planar 4:1 contraction for several values of Reynolds and Ericksen numbers.

AB - A finite difference method for solving nematic liquid crystal flows under the effect of a magnetic field is developed. The dynamic equations of nematic liquid crystals, given by the Ericksen–Leslie dynamic theory, are employed. These are expressed in terms of primitive variables and solved employing the ideas behind the GENSMAC methodology (Tomé and McKee, 1994; Tomé et al., 2002) [38,41]. These equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum. By employing fully developed flow assumptions an analytic solution for steady 2D-channel flow is found. The resulting numerical technique was then, in part, validated by comparing numerical solutions against this analytic solution. Convergence results are presented. To demonstrate the capabilities of the numerical method, the flow of a nematic liquid crystal through various complex geometries are then simulated. Results are obtained for L-shaped channels and planar 4:1 contraction for several values of Reynolds and Ericksen numbers.

KW - two-dimensional flow

KW - Ericksen-Leslie equations

KW - nematic liquid crystal

KW - analytic solution

KW - finite difference

UR - http://www.scopus.com/inward/record.url?scp=84877803527&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2013.03.061

DO - 10.1016/j.jcp.2013.03.061

M3 - Article

VL - 247

SP - 109

EP - 136

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -