We present a convex-splitting scheme for the fourth order parabolic equation
derived from a diffuse interface model with Peng-Robinson equation of state for
pure substance. The semi-implicit scheme is proven to be uniquely solvable, mass conservative,
unconditionally energy stable and L
∞ convergent with the order of O(∆t+
). The numerical results verify the effectiveness of the proposed algorithm and also
show good agreement of the numerical solution with laboratory experimental results.