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Energy-law Preserving Continuous Finite Element Methods for Simulation of Liquid Crystal and Multi-phase Flows

林平 教授

University of Dundee, UK

University of Science & Technology Beijing




The liquid crystal (LC) flow model is a coupling between orientation (director field) of LC molecules and a flow field. We propose a simple C^0 finite element formulation in space and a modified midpoint scheme in time which accurately preserves the inherent energy law of the model. We emphasise the energy law preservation because from the PDE analysis point of view the energy law is very important to correctly catch the evolution of singularities in the LC molecule orientation. Then, the idea is generalized to the Cahn-Hilliard phase field model where the biharmonic operator is decomposed into two Laplacian operators. A number of numerical examples demonstrate the good performance of the method. At the end of the talk we will show how to incorporate the temperature into the model and how to apply the method to a superconductivity model, especially at the regime of Hc2 or beyond. The talk is based on a few joint papers with Chun Liu, Qi Wang, Xingbin Pan and Roland Glowinski, etc.




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