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dc.contributor.authorFan, Xiaolin
dc.contributor.authorKou, Jisheng
dc.contributor.authorQiao, Zhonghua
dc.contributor.authorSun, Shuyu
dc.date.accessioned2017-03-20T08:46:08Z
dc.date.available2017-03-20T08:46:08Z
dc.date.issued2017-01-19
dc.identifier.citationFan X, Kou J, Qiao Z, Sun S (2017) A Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State. SIAM Journal on Scientific Computing 39: B1–B28. Available: http://dx.doi.org/10.1137/16M1061552.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/16M1061552
dc.identifier.urihttp://hdl.handle.net/10754/623029
dc.description.abstractThis paper presents a componentwise convex splitting scheme for numerical simulation of multicomponent two-phase fluid mixtures in a closed system at constant temperature, which is modeled by a diffuse interface model equipped with the Van der Waals and the Peng-Robinson equations of state (EoS). The Van der Waals EoS has a rigorous foundation in physics, while the Peng-Robinson EoS is more accurate for hydrocarbon mixtures. First, the phase field theory of thermodynamics and variational calculus are applied to a functional minimization problem of the total Helmholtz free energy. Mass conservation constraints are enforced through Lagrange multipliers. A system of chemical equilibrium equations is obtained which is a set of second-order elliptic equations with extremely strong nonlinear source terms. The steady state equations are transformed into a transient system as a numerical strategy on which the scheme is based. The proposed numerical algorithm avoids the indefiniteness of the Hessian matrix arising from the second-order derivative of homogeneous contribution of total Helmholtz free energy; it is also very efficient. This scheme is unconditionally componentwise energy stable and naturally results in unconditional stability for the Van der Waals model. For the Peng-Robinson EoS, it is unconditionally stable through introducing a physics-preserving correction term, which is analogous to the attractive term in the Van der Waals EoS. An efficient numerical algorithm is provided to compute the coefficient in the correction term. Finally, some numerical examples are illustrated to verify the theoretical results and efficiency of the established algorithms. The numerical results match well with laboratory data.
dc.description.sponsorshipThe work of the first and fourth authors was supported by funding from King Abdullah University of Science and Technology (KAUST). The work of the second author was partially supported by National Natural Science Foundation of China (11301163). The work of the third author was partially supported by Hong Kong Research Grant Council GRF grants 509213, 15302214 and NSFC/RGC joint research scheme N HKBU204/12.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/16M1061552
dc.rightsArchived with thanks to SIAM Journal on Scientific Computing
dc.subjectConvex splitting
dc.subjectEquation of state
dc.subjectMulticomponent two-phase systems
dc.subjectPeng-Robinson EoS
dc.subjectSequential splitting
dc.subjectVan der Waals EoS
dc.titleA Componentwise Convex Splitting Scheme for Diffuse Interface Models with Van der Waals and Peng--Robinson Equations of State
dc.typeArticle
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalSIAM Journal on Scientific Computing
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei, 432000, , China
dc.contributor.institutionDepartment of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, , Hong Kong
kaust.personFan, Xiaolin
kaust.personSun, Shuyu
refterms.dateFOA2018-06-13T18:14:42Z
dc.date.published-online2017-01-19
dc.date.published-print2017-01


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