In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state (EOS) for pure substance. The mass conservation, energy decay property, unique solvability and L∞ convergence of these two schemes are proved. Numerical results demonstrate the good approximation of the fourth order equation and confirm reliability of these two schemes.
- Diffuse interface model
- Energy stability
- Fourth order parabolic equation
ASJC Scopus subject areas
- Computational Mathematics