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    Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

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    Type
    Article
    Authors
    Kou, Jisheng cc
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2014-03-22
    Online Publication Date
    2014-03-22
    Print Publication Date
    2014-09
    Permanent link to this record
    http://hdl.handle.net/10754/564889
    
    Metadata
    Show full item record
    Abstract
    Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.
    Citation
    Kou, J., & Sun, S. (2014). Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media. Numerical Methods for Partial Differential Equations, 30(5), 1674–1699. doi:10.1002/num.21817
    Sponsors
    Contract grant sponsor: National Natural Science Foundation of China; contract grant number: 11301163Contract grant sponsor: Key Project of Chinese Ministry of Education; contract grant number: 212109Contract grant sponsor: KAUST research fund
    Publisher
    Wiley
    Journal
    Numerical Methods for Partial Differential Equations
    DOI
    10.1002/num.21817
    ae974a485f413a2113503eed53cd6c53
    10.1002/num.21817
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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