Translating Circle

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[0]
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 $\text{[math]}$ . The immersed boundary method is used to solve for the $\text{[math]}$ , $\text{[math]}$ and $\text{[math]}$ flows. And the potential solver (assumes irrotational flow) is used to solve for $\text{[math]}$ . The results are presented in the table below:

$\text{[math]}$	$\text{[math]}$

$\text{[math]}$

$\text{[math]}$	$\text{[math]}$

There is an inverse correlation between boundary thickness and Reynolds number as expected

Note

You can view the simulations at higher resolution by Right Click->View Image (on Firefox) or using an equivalent method on another browser.