Flow around a circular cylinder
The flow around a (geometrically) two-dimensional circular cylinder is case that has been used both as a validation case and as a legitimate research case. At very low Reynolds numbers, the flow is steady and symmetrical. As the Reynolds number is increased, asymmetries and time-dependence develop, eventually resulting the famous Von Karmann vortex street, and then on to turbulence. The problem geometry is two-dimensional and there is some variation in the details (both geometry and boundary conditions) that can be used. A typical geometry is shown below (not to scale).
The exterior boundaries are generally placed very far from the cylinder surface to avoid interaction between the boundary conditions. Grid generation is not especially difficult, though care must be taken to properly resolve the near-wall region as the Reynolds number is increased.
This problem has been solved as both a laminar flow and a turbulent flow. The DNS, LES, and the transitional cases are still considered a research cases. Many different numerical techniques have been used to solve this problem, but one usual comparison is the the resulting Strouhal frequency (if the simulation is in the proper Reynolds number range.
Many variations on the geometry are possible. One can impose symmetry by cutting the solution domain in half (along the x-direction). This will reduce the computational burden, but will reduce the range of physical applicability of the simulations (asymmetries develop at rather moderate Reynolds numbers). Another variation it to impose periodic conditions in the y-direction - which gives us an array of cylinders rather than just one cylinder. There has also been work done simulating the response of spinning cylinders both in a free stream and near walls.