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Convergence Analysis of Numerical Schemes for Liquid Crystals Based on the Invariant Energy Quadratization Method

thesis
posted on 2023-09-07, 20:58 authored by Yukun YueYukun Yue

This thesis investigates numerical methods for various Q-tensor models of nematic liquid crystals. Originating from the Landau-de Gennes theory, the numerical discretization of the Q-tensor model presents challenges due to its high non-linearity. The thesis investigates three distinct models, each capturing the behavior of liquid crystals under different conditions: the Q-tensor model, the Q-tensor model with inertia, and the Beris-Edwards model, which connects the Q-tensor model to the Navier-Stokes equation. The numerical methods utilized are based on the Invariant Energy Quadratization (IEQ) method, a recently developed technique extensively employed in constructing energy-stable numerical schemes for gradient-flow type problems. Our studies establish several properties of the proposed methods, such as stability, convergence, and convergence rates.  

Funding

Design and Analysis of Structure Preserving Discretizations to Simulate Pattern Formation in Liquid Crystals and Ferrofluids

Directorate for Mathematical & Physical Sciences

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Collaborative Research: GCR: Collective Behavior and Patterning of Topological Defects: From String Theory to Crystal Plasticity

Directorate for Mathematical & Physical Sciences

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History

Date

2023-08-15

Degree Type

  • Dissertation

Department

  • Mathematical Sciences

Degree Name

  • Doctor of Philosophy (PhD)

Advisor(s)

Franziska Weber

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