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

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    Type
    Article
    Authors
    Kou, Jisheng cc
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2015-07-16
    Online Publication Date
    2015-07-16
    Print Publication Date
    2015-01
    Permanent link to this record
    http://hdl.handle.net/10754/577322
    
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    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.
    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
    DOI
    10.1137/140969579
    Additional Links
    http://epubs.siam.org/doi/10.1137/140969579
    ae974a485f413a2113503eed53cd6c53
    10.1137/140969579
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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