A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations
Type
ArticleKAUST Department
VCC Analytics Research GroupVisual Computing Center (VCC)
Date
2018-08-23Online Publication Date
2018-08-23Print Publication Date
2018Permanent link to this record
http://hdl.handle.net/10754/630091
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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 outCitation
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_5Publisher
Springer NaturearXiv
1807.00328Additional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-99639-4_5ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-99639-4_5