  In this paper, we present energy-stable numerical schemes for a Smectic-A
liquid crystal model. This model involve the hydrodynamic velocity-pressure
macroscopic variables $({\bf u},p)$ and the microscopic order parameter of
Smectic-A liquid crystals, where its molecules have a uniaxial orientational
order and a positional order by layers of normal and unitary vector ${\bf n}$.
  We start from the formulation given in \cite{E} by using the so-called layer
variable $\phi$ such that ${\bf n}=\nabla \phi$ and the level sets of $\phi$
describe the layer structure of the Smectic-A liquid crystal. Then, a strongly
non-linear parabolic system is derived coupling velocity and pressure unknowns
of the Navier-Stokes equations $({\bf u},p)$ with a fourth order parabolic
equation for $\phi$.
  We will give a reformulation as a mixed second order problem which let us to
define some new energy-stable numerical schemes, by using second order finite
differences in time and $C^0$-finite elements in space. Finally, numerical
simulations are presented for $2D$-domains, showing the evolution of the system
until it reaches an equilibrium configuration.
  Up to our knowledge, there is not any previous numerical analysis for this
type of models.
