Steady Potential Flow through Box with Staggered Inlet and Outlet

Consider the flow through a two-dimensional box with staggered inlet and outlet as show in the figure below:
The flow enters and exits the box with a uniform speed . The aspect ratio of the box is .
The Demonstration plots the streamlines for this potential flow for a user-set value of .
These streamlines are the solution of the equation subject to the boundary conditions:
BC1: at , for and for ,
BC2: at , for and for ,
BC3: at , for , and
BC4: at , for .
The solution methodology is based on Chebyshev orthogonal collocation with collocation points.
This problem also admits an analytical solution given by T. Bennett [1]:
,
where . We have found excellent agreement between our numerical solution and the analytical solution.

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DETAILS

Reference
[1] T. Bennett, Transport by Advection and Diffusion, New York: Wiley, 2012.
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