Step5LinearConvection2D.py

from mpl_toolkits.mplot3d import Axes3D    
import numpy
from matplotlib import pyplot
from matplotlib import cm 
import time


nx = 81
ny = 81
nt = 100
c = 1
dx = 2 / (nx - 1)
dy = 2 / (ny - 1)
sigma = .2
dt = sigma * dx

x = numpy.linspace(0, 2, nx)
y = numpy.linspace(0, 2, ny)

u = numpy.ones((ny, nx))
un = numpy.ones((ny, nx)) 


u[int(.5 / dy):int(1 / dy + 1),int(.5 / dx):int(1 / dx + 1)] = 2 


fig = pyplot.figure(figsize=(11, 7), dpi=100)
ax = fig.gca(projection='3d')                      
X, Y = numpy.meshgrid(x, y)                            
surf = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)
pyplot.show();



t = time.time()
u = numpy.ones((ny, nx))
u[int(.5 / dy):int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2

for n in range(nt + 1): 
    un = u.copy()
    row, col = u.shape
    for j in range(1, row):
        for i in range(1, col):
            u[j, i] = (un[j, i] - (c * dt / dx * (un[j, i] - un[j, i - 1])) -
                                  (c * dt / dy * (un[j, i] - un[j - 1, i])))
            u[0, :] = 1
            u[-1, :] = 1
            u[:, 0] = 1
            u[:, -1] = 1

fig = pyplot.figure(figsize=(11, 7), dpi=100)
ax = fig.gca(projection='3d')
surf2 = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)
pyplot.show();
print('The Calculation with loops took: ' + str('{0:.2f}'.format(time.time() - t)) + 's')





t = time.time()
u = numpy.ones((ny, nx))
u[int(.5 / dy):int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2

for n in range(nt + 1): 
    un = u.copy()
    u[1:, 1:] = (un[1:, 1:] - (c * dt / dx * (un[1:, 1:] - un[1:, :-1])) -
                              (c * dt / dy * (un[1:, 1:] - un[:-1, 1:])))
    u[0, :] = 1
    u[-1, :] = 1
    u[:, 0] = 1
    u[:, -1] = 1

fig = pyplot.figure(figsize=(11, 7), dpi=100)
ax = fig.gca(projection='3d')
surf2 = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)
pyplot.show();
print('The Calculation with arrays took: ' + str('{0:.2f}'.format(time.time() - t)) + 's')