Investigation of Difference Schemes for Two-Dimensional Navier–Stokes Equations by Using Computer Algebra Algorithms

Abstract A class of consistent difference schemes for incompressible Navier–Stokes equations in physical variables and their differential approximations are considered using an algorithm for Gröbner basis construction. Results of investigating the first differential approximations of these schemes, which are obtained by using the authors' programs implemented in the SymPy computer algebra system, are presented. For the difference schemes under consideration, the quadratic dependence of the error for large Reynolds numbers and the inversely proportional dependence for creeping currents are analyzed.