  In this paper, we consider the numerical approximations for a hydrodynamical
model of smectic-A liquid crystals. The model, derived from the variational
approach of the modified Oseen-Frank energy, is a highly nonlinear system that
couples the incompressible Navier-Stokes equations and a constitutive equation
for the layer variable. We develop two linear, second-order time-marching
schemes based on the "Invariant Energy Quadratization" method for nonlinear
terms in the constitutive equation, the projection method for the Navier-Stokes
equations, and some subtle implicit-explicit treatments for the convective and
stress terms. Moreover, we prove the well-posedness of the linear system and
their unconditionally energy stabilities rigorously. Various numerical
experiments are presented to demonstrate the stability and the accuracy of the
numerical schemes in simulating the dynamics under shear flow and the magnetic
field.
