dc.contributor.author Kou, Jisheng dc.contributor.author Sun, Shuyu dc.date.accessioned 2019-03-17T12:02:22Z dc.date.available 2018-03-15T11:35:52Z dc.date.available 2019-03-17T12:02:22Z dc.date.issued 2018-07-05 dc.identifier.citation Kou J, Sun S (2018) Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state. Computer Methods in Applied Mechanics and Engineering 341: 221–248. Available: http://dx.doi.org/10.1016/j.cma.2018.06.002. dc.identifier.issn 0045-7825 dc.identifier.doi 10.1016/j.cma.2018.06.002 dc.identifier.uri http://hdl.handle.net/10754/627322 dc.description.abstract In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with the general reference velocity is derived rigorously through thermodynamical laws and Onsager’s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation between the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex–concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method. dc.description.sponsorship The work is supported in part by funding from King Abdullah University of Science and Technology (KAUST) through the grants BAS/1/1351-01, URF/1/2993-01, and REP/1/2879-01. dc.publisher Elsevier BV dc.relation.url https://www.sciencedirect.com/science/article/pii/S0045782518302998 dc.rights NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, [, , (2018-07-05)] DOI: 10.1016/j.cma.2018.06.002 . © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject Multi-component two-phase flow dc.subject Non-isothermal flow dc.subject Entropy stability dc.subject Convex splitting dc.title Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state dc.type Article dc.contributor.department Computational Transport Phenomena Lab dc.contributor.department Earth Science and Engineering Program dc.contributor.department Physical Science and Engineering (PSE) Division dc.identifier.journal Computer Methods in Applied Mechanics and Engineering dc.eprint.version Post-print dc.contributor.institution School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China dc.identifier.arxivid 1802.09020 kaust.person Sun, Shuyu kaust.grant.number BAS/1/1351-01 kaust.grant.number URF/1/2993-01 kaust.grant.number REP/1/2879-01 refterms.dateFOA 2018-06-14T03:50:39Z dc.date.published-online 2018-07-05 dc.date.published-print 2018-11 dc.date.posted 2018-02-25
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