A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State

Jisheng Kou, Shuyu Sun, Xiuhua Wang

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38 Scopus citations


The Peng--Robinson equation of state (PR-EoS) has become one of the most extensively applied equations of state in chemical engineering and the petroleum industry due to its excellent accuracy in predicting the thermodynamic properties of a wide variety of materials, especially hydrocarbons. Although great effort has been made to construct efficient numerical methods for the diffuse interface models with PR-EoS, there is still not a linear numerical scheme that can be proved to preserve the original energy dissipation law. In order to pursue such a numerical scheme, we propose a novel energy factorization (EF) approach, which first factorizes an energy function into a product of several factors and then treats the factors using their properties to obtain the semi-implicit linear schemes. We apply the EF approach to deal with the Helmholtz free energy density determined by PR-EoS, and then propose a linear semi-implicit numerical scheme that inherits the original energy dissipation law. Moreover, the proposed scheme is proved to satisfy the maximum principle in both time semidiscrete form and cell-centered finite difference fully discrete form under certain conditions. Numerical results are presented to demonstrate the stability and efficiency of the proposed scheme.
Original languageEnglish (US)
Pages (from-to)B30-B56
Number of pages1
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - Jan 7 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by the Scientific and Technical Research Project of Hubei Provincial Department of Education through grant D20192703.


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