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    Linearly Decoupled Energy-Stable Numerical Methods for Multicomponent Two-Phase Compressible Flow

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    Type
    Article
    Authors
    Kou, Jisheng
    Sun, Shuyu cc
    Wang, Xiuhua
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    BAS/1/1351-01
    URF/1/2993-01
    REP/1/2879-01
    Date
    2018-11-15
    Online Publication Date
    2018-11-15
    Print Publication Date
    2018-01
    Permanent link to this record
    http://hdl.handle.net/10754/629934
    
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    Abstract
    In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multicomponent two-phase compressible flow with a realistic equation of state (e.g., Peng--Robinson equation of state). The methods are constructed based on the scalar auxiliary variable (SAV) approaches for Helmholtz free energy and the intermediate velocities that are designed to decouple the tight relationship between velocity and molar densities. The intermediate velocities are also involved in the discrete momentum equation to ensure consistency with the mass balance equations. Moreover, we propose a componentwise SAV approach for a multicomponent fluid, which requires solving a sequence of linear, separate mass balance equations. The fully discrete schemes are also constructed based on the finite difference/volume methods with the upwind scheme on staggered grids. We prove that the semidiscrete and fully discrete schemes preserve the unconditional energy-dissipation feature. Numerical results are presented to verify the effectiveness of the proposed methods.
    Citation
    Kou J, Sun S, Wang X (2018) Linearly Decoupled Energy-Stable Numerical Methods for Multicomponent Two-Phase Compressible Flow. SIAM Journal on Numerical Analysis 56: 3219–3248. Available: http://dx.doi.org/10.1137/17m1162287.
    Sponsors
    This work was supported by funding from King Abdullah University of Science and Technology (KAUST) through grants BAS/1/1351-01, URF/1/2993-01, and REP/1/2879-01.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Numerical Analysis
    DOI
    10.1137/17m1162287
    Additional Links
    https://epubs.siam.org/doi/10.1137/17M1162287
    ae974a485f413a2113503eed53cd6c53
    10.1137/17m1162287
    Scopus Count
    Collections
    Articles; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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