A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State
KAUST DepartmentComputational Transport Phenomena Lab
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Preprint Posting Date2019-03-21
Online Publication Date2020-01-07
Print Publication Date2020-01
Permanent link to this recordhttp://hdl.handle.net/10754/660650
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AbstractThe 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.
CitationKou, J., Sun, S., & Wang, X. (2020). A Novel Energy Factorization Approach for the Diffuse-Interface Model with Peng--Robinson Equation of State. SIAM Journal on Scientific Computing, 42(1), B30–B56. doi:10.1137/19m1251230
SponsorsThis work was supported by the Scientific and Technical Research Project of Hubei Provincial Department of Education through grant D20192703.