A reference solution of the flow over a circular cylinder at Re = 40

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.

► A reference solution is provided for one of the most popular benchmark in CFD.
► Highly accurate numerical methods are used with a new set of boundary conditions.
► A user-friendly file gives the solution at any location with the spectral accuracy.
► Body-fitted and immersed boundary approaches are compared.
► Numerical errors and convergence for the velocity and the pressure are investigated.