AFMM Poisson 2D

"""
Handling imports
"""
import os
import sys

sys.path.append(os.path.dirname(os.getcwd()))

from computational import finite_difference
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

"""
Setting up the dimensions of the grid
and the point distribution
"""
dx = 0.2
dy = 0.2
Lx = 1
Ly = 1

num_x = int(Lx / dx)
num_y = int(Ly / dy)

"""
Creating new grid with defined size and number of points
"""

grids = finite_difference()

grids.cartesian((Lx, Ly, 1), (num_x, num_y, 1))

grids.initialize()

grids.transmissibility()

"""
Setting the solver to use second order derivative for the equation
"""
grids.central(order=2)

"""
Integrating the boundary conditions
 (b0, b1, f)
 (1 , 0 , 0)
"""
grids.implement_bc(b_xmin=(1, 0, 0),
                   b_xmax=(1, 0, 0),
                   b_ymin=(1, 0, 10),
                   b_ymax=(1, 1, 5))

"""
Calculating the right hand side
"""
rhs = [r[0]**2 for r in grids.center]

"""
Calculating the boundary conditions
"""
grids.solve(rhs=rhs)


"""
Plotting the results
"""

X = grids.center[:, 0].reshape(num_x, num_y)
Y = grids.center[:, 1].reshape(num_x, num_y)

Z = grids.unknown.reshape(num_x, num_y)

plt.contourf(X, Y, Z, range(0,11),
             alpha=1, cmap=cm.hot, vmin=0, vmax=10)
plt.colorbar()

plt.title('Figure 1, velocity distribution', fontsize=14)
plt.xlabel('x-axis', fontsize=14)
plt.ylabel('y-axis', fontsize=14)

plt.xlim([0, 1])
plt.ylim([0, 1])

plt.show()