ACSI Update: Diffusion Code Output

Here is the output of the 2D diffusion code when alpha = .1 on a 1X1 rectangular region at an initial condition of 1 and zero at the boundaries. Time varies from 0 to 5. The data points are graphed using JMP, which can import the .dat file directly with very little effort! Note that the solution diverges rapidly when alpha is too large compared to the time step or the number of grid elements is too small compared to the time step. This problem is solved with 10001 time steps and a 51X51 grid partition.

The Fortran source code is given in my Thursday, October 27, 2011 post titled ACSI Update: 2D Diffusion Solver

PDE: Ut = alpha^2 * (Uxx + Uyy)     0 <_ t <_ 5,     0 <_ x <_ 1,     0 <_ y <_ 1
BCs: U(0, y, t) = 0
         U(1, y, t) = 0
         U(x, 0, t) = 0
         U(x, 1, t) = 0
IC: U(x, y, 0) = 1

t = 0

t = 1

 

 t = 2

t= 3

t = 4

t = 5