Energy Stable Linear Schemes for Mass-Conserved Gradient Flows with Peng-Robinson Equation of State

Abstract

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.