We now consider the periodic translation of a rigid circle. Its boundary is described by:
with a periodic shape function
The code listing
shapevariables = ( lambda t: 0.5*sin(t), ) X = lambda s,q: cos(s) + q Y = lambda s,q: sin(s) bodies = ( (X,Y), )
Due to Stoke’s Paradox there does not exist a 2D creeping flow around a translating cylinder that vanishes at infinity. The Stokesian solver handles this problem gracefully and outputs a uniform flow for . The immersed boundary method is used to solve for the , and flows. And the potential solver (assumes irrotational flow) is used to solve for . The results are presented in the table below:
There is an inverse correlation between boundary thickness and Reynolds number as expected
You can view the simulations at higher resolution by Right Click->View Image (on Firefox) or using an equivalent method on another browser.