AbstractNine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two‐dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid‐driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non‐staggered grid scheme with higher‐order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so‐called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non‐staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory ov