### Abstract

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

Pages (from-to) | 1-14 |

Number of pages | 15 |

Journal | BIT Numerical Mathematics |

Volume | 56 |

Issue number | 2 |

Early online date | 13 Nov 2015 |

DOIs | |

Publication status | Published - 1 Jun 2016 |

### Fingerprint

### Keywords

- computational fluid dynamics
- nematic liquid crystal
- complex fluids
- iterative solvers
- alignment tensor

### Cite this

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*BIT Numerical Mathematics*, vol. 56, no. 2, pp. 1-14. https://doi.org/10.1007/s10543-015-0586-5

**Computational fluid dynamics for nematic liquid crystals.** / Ramage, Alison; Sonnet, Andre M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Computational fluid dynamics for nematic liquid crystals

AU - Ramage, Alison

AU - Sonnet, Andre M.

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-015-0586-5

PY - 2016/6/1

Y1 - 2016/6/1

N2 - Due to recent advances in fast iterative solvers in the field of computational fluid dynamics, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex fluid such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier-Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convection-diffusion type equation with non-linear terms that stem from a Landau-Ginzburg-DeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.

AB - Due to recent advances in fast iterative solvers in the field of computational fluid dynamics, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex fluid such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier-Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convection-diffusion type equation with non-linear terms that stem from a Landau-Ginzburg-DeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.

KW - computational fluid dynamics

KW - nematic liquid crystal

KW - complex fluids

KW - iterative solvers

KW - alignment tensor

UR - http://link.springer.com/journal/volumesAndIssues/10543

U2 - 10.1007/s10543-015-0586-5

DO - 10.1007/s10543-015-0586-5

M3 - Article

VL - 56

SP - 1

EP - 14

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 2

ER -