Thermodynamically consistent simulation of nonisothermal diffuse-interface two-phase flow with Peng–Robinson equation of state

Jisheng Kou, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


In this paper, we consider a diffuse-interface gas–liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng–Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas–liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, thereby deriving a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex–concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method.
Original languageEnglish (US)
Pages (from-to)581-605
Number of pages25
JournalJournal of Computational Physics
StatePublished - Jun 14 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): BAS/1/1351-01-01
Acknowledgements: This work is supported by National Natural Science Foundation of China (No. 11301163) and by funding from King Abdullah University of Science and Technology (KAUST) through the grant BAS/1/1351-01-01. Research was partially completed while the corresponding author (S. Sun) was visiting the Institute for Mathematical Sciences, National University of Singapore in 2018.


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