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    A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations

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    Type
    Article
    Authors
    Blinkov, Yury A.
    Gerdt, Vladimir P.
    Lyakhov, Dmitry cc
    Michels, Dominik L.
    KAUST Department
    VCC Analytics Research Group
    Visual Computing Center (VCC)
    Date
    2018-08-23
    Online Publication Date
    2018-08-23
    Print Publication Date
    2018
    Permanent link to this record
    http://hdl.handle.net/10754/630091
    
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    Abstract
    We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first two authors is based on a combination of the finite volume method, difference elimination, and numerical integration. We make use of the techniques of the differential and difference Janet/Gröbner bases. In order to prove strong consistency of the generated scheme we correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. Additionally, we compute the modified differential system of the obtained scheme and analyze the scheme’s accuracy and strong consistency by considering this system. An evaluation of our scheme against the established marker-andcell method is carried out
    Citation
    Blinkov, Y. A., Gerdt, V. P., Lyakhov, D. A., & Michels, D. L. (2018). A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations. Lecture Notes in Computer Science, 67–81. doi:10.1007/978-3-319-99639-4_5
    Publisher
    Springer Nature
    Journal
    Computer Algebra in Scientific Computing
    DOI
    10.1007/978-3-319-99639-4_5
    arXiv
    1807.00328
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-99639-4_5
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-99639-4_5
    Scopus Count
    Collections
    Articles; Visual Computing Center (VCC)

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