Partial Diff equation Solve partial differential^2 T/partial differential x^2 +
ID: 3141288 • Letter: P
Question
Partial Diff equation Solve partial differential^2 T/partial differential x^2 + partial differential^2 T/partial differential y^2 = partial differential T/partial differential for the cell 3 x 3 shown. The top and are insulated while the bottom is set to T = 1. The cells are all h x h with h^z/Delta = 1. If at = 0 all cell temperatures = 2 write a set of 9 equations which will allow you to compute T at time Delta K. Use implicit time dating. Input to cell 5 in x direction h (1) [T^(1)_ 4 - T^(1)_5]/Delta h output of cell 5 in x direction h(1) [T^(1)_5 - T^(1)_6]/h Input to cell 2 in y direction h(1) [1 - T^(1)_2]/(h/2) Accumulation in cell 5 h^2 (1)_cell volume [T^(1)_5 - 2]/Delta Do one pass of over relation through the 9 equations you derived, starting cell and ending at cell # 9, 1, 2, 3, 4, 5, 6, 7, 8, 9. Initial for SOR is Temperature @ = 0.Explanation / Answer
The SOR method is a variant of Gauss Seidal method --
Ti,j(n+1) = Ti,j(n+1) + (1/4)*wRi,j = (1/4)*w*[ Ti-1,j(n+1) + Ti+1,j(n) + Ti,-1(n+1) + Ti,j+1(n) ] + (1-w)*Ti,j(n)
where w is the Accelerating factor .
superscripts show no. of increments/advancements in time .
Let us start from i=1 , j=1 ,n=1
T1,1(n+1)= (1/4)*w*[ T0,1(1) + T 1,1(0) + T0( 1) + T0, 1(0) ] + (1-w)*T1,1(0)
T at i=0,j=0 or n=0 denote boundary values .
Similarly for i=1 ,j=2,n=0 ,
.....................
for i=1 ,j=3,n=0 ,
.........................
for i=2 ,j=1,n=0
for i=2 ,j=2,n=0
for i=2 ,j=3,n=0
for i=3 ,j=1,n=0
for i=3 ,j=2,n=0
for i=3 ,j=3,n=0