  For the first time the electrohydrodynamic convection (EHC) of nematic liquid
crystals is studied via fully nonlinear simulation. As a system of rich
pattern-formation the EHC is mostly studied with negative nematic liquid
crystals experimentally, and sometimes with the help of theoretical instability
analysis in the linear regime. Up to now there is only weakly nonlinear
simulation for a step beyond the emergence of steady convection rolls. In this
work we modify the liquid crystal stochastic rotational model (LC SRD) [Lee et
al., J. Chem. Phys., 2015, 142, 164110] to incorporate the field alignment
mechanism for positive and negative nematic liquid crystals. The convection
patterns and their flow dynamics in the presence of external electric field are
studied. Our results predict the similar optical convection patterns in the
reflected polarized light when one uses positive and negative types of nematic
liquid crystals. However in the emerged flow fields, surprisingly, the driving
areas of convection rolls are different for different types of LCs. Their
application for nematic colloidal transportation in microfluidics is discussed.
