A Numerical Experiment In The Limit of Zero Reynolds Number For Flow Around A Circular Cylinder*

The Stokes flow around a circular cylinder has not been extensively studied with a numerical experiment. The reason is that the flow domain must very large, in order to let the viscous force develop freely both usptream of the cylinder and in the transverse direction. In a recent publication of our group, we were able to determine the onset of flow separation for this flow at Re > 6.36 with a domain that extends eight orders of magnitude with respect to the cylinder diameter. It is expected that the domain needed to study this flow for lower Reylolds numbers should be many more orders of magnitude greater than in that work. For this purpose, we have designed a computational mesh with transition elements that enables the elements to have an aspect ratio of 1:1 in order to maintain accuracy of the computations. The design is going to be thoroughly discussed along with the results for a Renolds number up to 10^-6. In addition, it is going to be shown that the undisturbed velocity profile penetrates deeply both in the streamwise and the transverse direction before it is distorted due to the action of the viscous force exerted at the walls of the cylinder.  The domain is fifteen orders of magnitude greater than the cylinder diameter. It is the first time that a flow is studied in a domain with these dimensions.  So far, it has been reported in the literature that the greatest possible domain for Stokes flow is six orders of magnitude with respect to the cylinder diameter. It should be also noted, that it s impossible to study this flow with a laboratory experiment. In other words, this study is a case example of how a numerical experiment can be used to acquire findamental knowledge in Fluid Mechanics.