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-infinity 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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We are grateful to Prof. Zhizhong Sun of Department of Mathematics of Southeast University and Prof. Hehu Xie of Institute of Computational Mathematics of Chinese Academy of Sciences for providing useful suggestions and many helpful discussions. The research of Zhonghua Qiao is partially supported by the Hong Kong Research Grant Council GRF grant 15302214, NSFC/RGC Joint Research Scheme N_HKBU204/12 and the Hong Kong Polytechnic University internal grant 1-ZE33. Shuyu Sun gratefully acknowledges that the research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST).