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This article presents a numerical algorithm based on the singular boundary method (SBM) for the incompressible steady Navier–Stokes equations formulated using primitive variables. The SBM with the Stokeslet fundamental solution and dual reciprocity (DR) principle has been chosen to solve the nonlinear flow equations. The particular solution of the non-homogeneous Stokes equations is constructed as a linear combination of implicitly local radial basis function. The simple direct iterative scheme was used to handle nonlinearities of Navier–Stokes equations with a variation of the non-homogeneous term of the particular solution. The non-homogeneous term is formed using the nonlinear convective terms of the momentum equations, evaluated using values from previous iterations. It is found that SBM with a localized DR principle gives reasonable results for numerical problems of lid-driven cavity flow up to Re = 3200, and the backward-facing step at Re = 800.

GLOBAL SINGULAR BOUNDARY METHOD FOR SOLVING 2D NAVIER–STOKES EQUATIONS