Run the Diffusion model

Use this notebook to demonstrate how to run the Diffusion model.

Before starting, make sure you've installed the bmi-live package in developer mode. Execute this statement at the command line (not in this notebook!):

$ python setup.py develop

Include one import that we'll use later:



In [1]:

    
import numpy as np

Start by importing the Diffusion class from the bmi-live package:



In [2]:

    
from bmi_live import Diffusion

Create an instance of the model:



In [3]:

    
m = Diffusion()

This instance uses default parameter values set up in the class. View them:



In [4]:

    
print('Number of columns:', m.nx)
print('Number of rows:', m.ny)
print('Spacing between columns:', m.dx)
print('Spacing between rows:', m.dy)
print('Diffusivity coefficient:', m.alpha)









    



Number of columns: 8
Number of rows: 6
Spacing between columns: 1.0
Spacing between rows: 1.0
Diffusivity coefficient: 0.9

What does the initial temperature array look like?



In [5]:

    
print(m.temperature)









    



[[0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0.]
 [0. 0. 0. 0. 0. 0. 0. 0.]]

Add an impulse to the initial temperature field:



In [6]:

    
m.temperature[3, 3] = 100.0

Check that the temperature field has been updated:



In [7]:

    
print(m.temperature)









    



[[  0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0. 100.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.   0.]]

Now advance the model by a single time step:



In [8]:

    
m.advance()

View the new state of the temperature field:



In [9]:

    
print(m.temperature)









    



[[ 0.     0.     0.     0.     0.     0.     0.     0.   ]
 [ 0.     0.     0.     0.     0.     0.     0.     0.   ]
 [ 0.     0.     0.     3.125  0.     0.     0.     0.   ]
 [ 0.     0.     3.125 87.5    3.125  0.     0.     0.   ]
 [ 0.     0.     0.     3.125  0.     0.     0.     0.   ]
 [ 0.     0.     0.     0.     0.     0.     0.     0.   ]]

There's diffusion!

Advance the model to some distant time:



In [10]:

    
distant_time = 10
for _ in range(distant_time):
    m.advance()

View the new state of the temperature field (with help from np.set_printoptions):



In [11]:

    
np.set_printoptions(formatter={'float': '{: 6.2f}'.format})
print(m.temperature)









    



[[  0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00]
 [  0.00   0.08   0.55   1.80   0.55   0.08   0.01   0.00]
 [  0.00   0.55   3.53  10.66   3.53   0.55   0.05   0.00]
 [  0.00   1.80  10.66  29.92  10.66   1.82   0.19   0.00]
 [  0.00   0.54   3.48  10.47   3.48   0.54   0.05   0.00]
 [  0.00   0.00   0.00   0.00   0.00   0.00   0.00   0.00]]

Note that temperature is set to zero at the boundaries.