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

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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
Original languageEnglish (US)
Pages (from-to)67-81
Number of pages15
JournalComputer Algebra in Scientific Computing
Volume11077 LNCS
DOIs
StatePublished - Aug 23 2018

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