这个作业是完成数学应用题
MATH0086 Coursework 3
如下图所示，将长圆柱体横向放置在两个平板之间的流场中
（左图）。 由于假定圆柱体较长，因此可以忽略最终效果，因此
流场是二维的，可以在垂直于轴心的平面上研究
圆筒。 假定流体不可压缩。 假定流动是无旋流的，
因此可以用满足拉普拉斯方程的标量流函数ψ来描述
∂
2ψ
∂x2
+
∂
2ψ
∂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?