Flow Around a Cylinder with Circulation

    Here is the Mathematica code to generate the animation for flow around a cylinder with circulation.

Needs["Graphics`PlotField`"] ; AnimateCirculationFlow[{xcenter_, ycenter_}, radius_, ... 754;$DisplayFunction],  {tau, 0, time, timestep}] ; Return[picture] ; ] ;

Here are some result.

AnimateCirculationFlow[{-2, 2}, 1/2, 10, 0.25] ;

Circulation (-2,2)

AnimateCirculationFlow[{-2, 1}, 1/2, 10, 0.25] ;

Circulation (-2,1)

AnimateCirculationFlow[{-2, 0}, 1/2, 10, 0.25] ;

Circulation (-2,0)

One interesting question that arises is what occurs when we speed up the circulation around the obstacle. To do so, we use the same technique, but simply adjust γ and the size of the viewing window. Here is γ = 7 viewed on [-5, 5] ×[-5, 5].

Needs["Graphics`PlotField`"] ; LargeAnimateCirculationFlow[{xcenter_, ycenter_}, rad ... 754;$DisplayFunction],  {tau, 0, time, timestep}] ; Return[picture] ; ] ;

This gives us the following interesting results.

LargeAnimateCirculationFlow[{-2, 4}, 1/2, 10, 0.25] ;

Large Circulation (-2,4)

LargeAnimateCirculationFlow[{-2, 3}, 1/2, 10, 0.25] ;

Large Circulation (-2,3)

LargeAnimateCirculationFlow[{-2, 2}, 1/2, 10, 0.25] ;

Large Circulation (-2,2)