First and second order numerical schemes for the fourth order parabolic equation with Peng-Robinson equation of state, which are based on recently proposed invariant energy quadratisation method are developed. Both schemes are linear, unconditionally energy stable and uniquely solvable. The reduced linear systems are symmetric
and positive definite, so that their solutions can be efficiently found. Numerical results
demonstrate the good performance of the schemes, consistent with experimental data.
Conservative gradient flow Peng-Robinson equation of state invariant energy quadratisation unconditional energy stability.