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Abstract: A ‘local’ radial basic function (RBF) based gridfree scheme has been developed to solve unsteady, incompressible Navier–Stokes equations in primitive variables. The velocity–pressure decoupling is obtained by making use of a fractional step algorithm. The scheme is validated over a variety of benchmark problems and found a very good agreement with the existing results. Comparisons with the benchmark solutions show that the developed local RBF gridfree scheme is stable and produces accurate results on domains discretized even with non-uniform distribution of nodal points. [Copyright &y& Elsevier]