import numpy as np
import matplotlib.pyplot as plt
import time, sys

"""
Simulation comments :
Since we doing diffusion, which is a isotropic phenomena, we add the central differences scheme to have a isotropic scheme.
"""

# Physical parameters.
vis = 0.3

# Spatial parameters.
nx, ny = 41, 41 # Number of grid points.
dx = 2 / (nx-1)	# Distance between any pair of adjacent grid points.

#Time parameters.
nt = 40	# Number of timesteps we want to calculate.
sigma = 0.3 # Sigma is a parameter defined later, but the resolution uses it.
#dt = 0.01	# Amount of time each timesteps covers (delta t)
dt = sigma * dx**2 / vis # dt is defined using sigma, see later lessons for the definition.
tT = dt*nt
print('Total time : ' + str(tT))
print(dx)

# Boundary conditions.
# Starting all values as 1 m/s.
u = np.ones(nx)
# Setting u = 2 between 0.5 and 1 as per out initial conditions.
u[int(0.5 / dx):int(1 / dx + 1)] = 2

# PLot initial conditions.
fig, ax = plt.subplots(nrows=1, ncols =2, sharey=True)

ax[0].plot(np.linspace(0,2,nx),u)

# Temporary array for the solutions.
un = np.ones(nx)

for n in range(nt):	# Loop for values of n from 0 to nt.
    un = u.copy()	# Copy the existing values of u into un.
    print('This is time step : ' + str(n))
    print(un)
    
    for i in range(1, nx-1): # Loop for values in u from 1 to nx -1
        u[i] = un[i] + vis * dt / (dx)**2 * (un[i+1]-2*un[i] + un[i-1])

# PLot the solution at t = t_final.
ax[1].plot(np.linspace(0,2,nx), u)

plt.show()