  The classical problem of the flow over a circular cylinder at Reynolds number
40 is considered using an accurate pseudo-spectral code. A new set of boundary
conditions is proposed to improve the representation of the infinite flow
domain, especially in the far wake area. It is shown that the resulting
accuracy of the computed flow allows its use as a reference solution for code
validation. This reference solution is reachable at any location up to 50
cylinder diameters far from the cylinder centre through spectral interpolation
with a user-friendly script provided in appendix. It is shown how this solution
offers the opportunity to perform a convergence study and to investigate the
spatial distribution of numerical errors. The main goal of this study is to
propose this reference solution as an helpful tool for numerical validation and
development, especially for the improvement of immersed boundary methods toward
high-order accuracy.
