Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

Handle URI:
http://hdl.handle.net/10754/577322
Title:
Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters
Authors:
Kou, Jisheng; Sun, Shuyu ( 0000-0002-3078-864X )
Abstract:
In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.
KAUST Department:
Computational Transport Phenomena Lab; Physical Sciences and Engineering (PSE) Division
Citation:
Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters 2015, 37 (4):B543 SIAM Journal on Scientific Computing
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
16-Jul-2015
DOI:
10.1137/140969579
Type:
Article
ISSN:
1064-8275; 1095-7197
Additional Links:
http://epubs.siam.org/doi/10.1137/140969579
Appears in Collections:
Articles; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorKou, Jishengen
dc.contributor.authorSun, Shuyuen
dc.date.accessioned2015-09-15T12:48:03Zen
dc.date.available2015-09-15T12:48:03Zen
dc.date.issued2015-07-16en
dc.identifier.citationNumerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters 2015, 37 (4):B543 SIAM Journal on Scientific Computingen
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/140969579en
dc.identifier.urihttp://hdl.handle.net/10754/577322en
dc.description.abstractIn this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a modified Newton's method for solving this nonlinear model and analyze its properties; we also analyze a finite element method with a physical-based adaptive mesh-refinement technique. Numerical examples are tested to verify the theoretical results and the efficiency of the proposed methods.en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/140969579en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectsurface tensionen
dc.subjectmulticomponent fluiden
dc.subjectgradient theoryen
dc.subjectNewton's methoden
dc.subjectadaptive finite element methoden
dc.titleNumerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parametersen
dc.typeArticleen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionSchool of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, Chinaen
dc.contributor.institutionSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, Chinaen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorSun, Shuyuen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.