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

Type
Article

Authors
Blinkov, Yury A.
Gerdt, Vladimir P.
Lyakhov, Dmitry
Michels, Dominik L.

KAUST Department
VCC Analytics Research Group
Visual Computing Center (VCC)

Online Publication Date
2018-08-23

Print Publication Date
2018

Date
2018-08-23

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
Lecture Notes in Computer Science

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

Permanent link to this record