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? influence of temporal discretization
Posted:
May 19, 2012 8:02 AM


Hi:
Suppose we have a diffusion eqn: dT/dt = a*div(grad(T))+Q in non dimensional form.
a ~ 1.0E6
Q changes with time and space. The problem is 3D, z is the depth direction.
The spatial form of Q is roughly a Gaussian function with equal standard deviation (STD) in x and y
directions and a larger STD in z direction; all these 3 STDs are small, i.e., the function is sharply
concentrated in a confimed spatial region.
The focus (or center) of Q moves raipdly in a target region. This region is a circle, and the focus
of Q moves spirially from the center of the circle to its boundary. At each (spatial) point, Q stays
only 0.1 sec, and then immediately moves to the next point. Q starts from time 0 and stops at
300 sec.
Now, we want to observe the saptial temperature profile at 500 sec. Can we discretize the time
using dt as 0.1 sec or should we use a dt even smaller? How do we estimate the appropriate
value of dt?
Thanks,



