MATH0086 Coursework 3

（左图）。 由于假定圆柱体较长，因此可以忽略最终效果，因此

∂x2
+

∂y2
= 0。
Because of biaxial symmetry we need to consider only a quarter of the full domain. On this
domain, ψ satisfies the boundary conditions given below (figure right), where u0 is the constant
inlet velocity and a is half the distance between the plates.
Using the Galerkin method, derive and solve the FE equation for the mesh shown below. Use
the global node numbering indicated. For the solution obtained, plot the contour lines in the
full domain of the flow.
Give some discussion to the computed solution (its physical sense, accuracy, …). How would
you improve the accuracy of the solution?

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