The two-dimensional (2-D) heat equation is given by du at (d²ud²u) ¹1 a x ² + √y ² = α

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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The two-dimensional (2-D) heat equation is given by
ди
at
= a
(d²u_d²u)\
əx² + dy ² )
(4.97)
Transcribed Image Text:The two-dimensional (2-D) heat equation is given by ди at = a (d²u_d²u)\ əx² + dy ² ) (4.97)
Apply the ADI scheme to the 2-D heat equation and find un+¹ at the internal grid points in the
mesh shown in Figure P4.2 for rx = ry= 2. The initial conditions are
u" =1-
u"=0
u" =1-.
x
3Ax
y
y
2Ay
i=1
along y = 0
and the boundary conditions remain fixed at their initial values.
FIGURE P4.2
along x = 0
everywhere else
2 3
Transcribed Image Text:Apply the ADI scheme to the 2-D heat equation and find un+¹ at the internal grid points in the mesh shown in Figure P4.2 for rx = ry= 2. The initial conditions are u" =1- u"=0 u" =1-. x 3Ax y y 2Ay i=1 along y = 0 and the boundary conditions remain fixed at their initial values. FIGURE P4.2 along x = 0 everywhere else 2 3
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