Semi-discrete energy-stable schemes for a tensor-based hydrodynamic model of nematic liquid crystal flows

Abstract

In this paper, we develop a first-order and a second-order coupled energy stable numerical scheme respectively for a Q-tensor based hydrodynamic model of nematic liquid crystal flows. We then extend the first order coupled scheme to a decoupled scheme and show that it is energy stable as well. The fully coupled schemes are implemented in 2-dimensional space and time, with which we study defect dynamics in flows of nematic liquid crystals in a channel. The numerical schemes are shown to be effective in solving the Q-tensor based liquid crystal model. The methodology developed here also provides a paradigm for developing energy-stable schemes for more general hydrodynamic models of complex fluids which obey an energy dissipation law.