  In this paper, a lattice Boltzmann model with the single-relaxation-time
model for the Cahn-Hilliard equation (CHE) is proposed. The discrete source
term is redesigned through a third-order Chapman-Enskog analysis. By coupling
the Navier-Stokes equations, the time-derivative term in the source term is
expressed as the relevant spatial derivatives. Furthermore, the source term on
the diffusive time scale is also proposed though recovering the macroscopic CHE
to third order. The model is tested by simulating diagonal motion of a circular
interface, Zalesak's disk rotation, circular interface in a shear flow and a
deformation field. It is shown that the proposed method can track the interface
with high accuracy and stability. For the complex flow, the source term on the
diffusive time scale should be considered for capturing the interface
correctly.
