Accurate critical Reynolds number for flow past a circular cylinder

The critical Rayleigh number for Rayleigh-Benard convection, and the critical Reynolds number for flow between parallel plates are known to high accuracy. But the critical Re for the prototypical bluff-body flow, namely two-dimensional steady flow past a circular cylinder in an unbounded domain, is not. Here, we systematically increase the upstream, downstream, and cross-stream extents of a rectangular domain, and use a spectral-element technique to efficiently achieve spatial convergence on a sequence of such domains. The results show that the upstream extent of the domain is very important, due to the effects of "blockage" on the computed steady base flow. Full domain, spatial, and temporal convergence provides a critical Reynolds number accurate to four significant digits. This result can be used as a special case for validating computations for variants of the "standard" circular cylinder case.