Title: A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations,
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/Groebner 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-and-cell method is carried out.