  We use a hybrid method of lattice Boltzmann and finite differences to
simulate flat and curved interfaces between the nematic and isotropic phases of
a liquid crystal described by the Landau-de Gennes theory. For the flat
interface, we measure the interfacial velocity at different temperatures around
the coexistence. We show that the interface is completely static at the
coexistence temperature and that the profile width is in line with the
theoretical predictions. The interface is stable in a range of temperatures
around coexistence and disappears when one of the two phases becomes
mechanically unstable. We stabilize circular nematic domains by a shift in
temperature, related to the Laplace pressure, and estimate the spurious
velocities of these lattice Boltzmann simulations.
