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 . 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:

im4 im5
 
im3  
im2 im1

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

Note

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