Now we have the program set up as we shown above, we can compare the result of the two level time stepping to our steady state problem from previous home work, irrespective of deta-t and theta at long time. The solution map is shown below.
The steady state solution map from direct solver:
The two level time stepping solution map after long time:
As we can see that, the to solution map is the same. Our two level time stepping method will reach the same state in long time as the steady state.
Now we will look into the effect of r and theta. With the given condition, we will compare:
For each condition we also picked out 5 points on the interior to compare the value changes of specific points with respect of time.
theta=0.0 and r=0.25
theta=0.0 r=0.25
theta=0.3, r=0.75
theta=0.3, r=1.50
theta=0.6, r=10.0
Based on my calculation the time constant can be estimate around 50 frame. and that times delta T is the time constant.
code: hw3t1