计算水力学

2n?????1、设有理想流体自左向右流动，设，流速势满足??0，边界条件：

AB:??10CD:??0ABCD:取

???0?n

?x??y?1，试计算流场离散网格节点上的?值，并给出等势线。

（代数方程组可

用简单迭代法或高斯—赛德尔迭代法求解）。

?2??2y???2?2?0?x?x?y解：，

2??y?1

??2??2??i?1,j?2?i,j??i?1,j??x?2?????i,j?1?2?i,j??i,j?12???y

即

?i,j1???i?1,j??i?1,j??i,j?1??i,j?1?4

??????????i,j?1??i?1,j?0?n?x?y边界条件

??x,0??10?(0,y)?0

?2u?2u2、椭圆型方程2?2?0 ?x??y?1

?x?y?1:U?10到1之间线性变化?2:U?0?u?0?n

解：?x??y?1，用Visual Basic 语言编写程序如下：

Private Sub Command1_Click() Dim a(5, 10) As Single Dim i, j As Integer For j = 0 To 10

a(0, j) = 0: a(5, j) = 1 Next j Do

For i = 0 To 3

a(i + 1, 0) = 0.2 * (i + 1) For j = 0 To 8

a(i + 1, 10) = a(i + 1, 9)

k = 0.25 * (a(i + 2, j + 1) + a(i, j + 1) + a(i + 1, j + 2) + a(i + 1, j)) m = a(i + 1, j + 1) - k a(i + 1, j + 1) = k Next j Next i

Loop While Abs(m) >= 0.0001 For i = 0 To 5 For j = 0 To 10

Print Format(a(i, j), \ Next j Print Next i End Sub

其中：Command1.Caption=椭圆型方程计算 运行结果如下：

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