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In this paper, we propose two efficient fully-discrete schemes for Q-tensorflow of liquid crystals by using the first- and second-order stabilizedexponential scalar auxiliary variable (sESAV) approach in time and the finitedifference method for spatial discretization. The modified discrete energydissipation laws are unconditionally satisfied for both two constructedschemes. A particular feature is that, for two-dimensional (2D) and a kind ofthree-dimensional (3D) Q-tensor flows, the unconditionalmaximum-bound-principle (MBP) preservation of the constructed first-orderscheme is successfully established, and the proposed second-order schemepreserves the discrete MBP property with a mild restriction on the time-stepsizes. Furthermore, we rigorously derive the corresponding error estimates forthe fully-discrete second-order schemes by using the built-in stabilityresults. Finally, various numerical examples validating the theoreticalresults, such as the orientation of liquid crystal in 2D and 3D, are presentedfor the constructed schemes.

Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals