  In this paper, we propose two efficient fully-discrete schemes for Q-tensor
flow of liquid crystals by using the first- and second-order stabilized
exponential scalar auxiliary variable (sESAV) approach in time and the finite
difference method for spatial discretization. The modified discrete energy
dissipation laws are unconditionally satisfied for both two constructed
schemes. A particular feature is that, for two-dimensional (2D) and a kind of
three-dimensional (3D) Q-tensor flows, the unconditional
maximum-bound-principle (MBP) preservation of the constructed first-order
scheme is successfully established, and the proposed second-order scheme
preserves the discrete MBP property with a mild restriction on the time-step
sizes. Furthermore, we rigorously derive the corresponding error estimates for
the fully-discrete second-order schemes by using the built-in stability
results. Finally, various numerical examples validating the theoretical
results, such as the orientation of liquid crystal in 2D and 3D, are presented
for the constructed schemes.
