A Convex-Splitting Scheme for a Diffuse Interface Model with Peng-Robinson Equation of State

Abstract

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 $\mathcal{O}(∆t+h^2)$. The numerical results verify the effectiveness of the proposed algorithm and also show good agreement of the numerical solution with laboratory experimental results.