Original file(1,200 × 954 pixels, file size: 2.66 MB, MIME type: image/gif, looped, 30 frames, 3.0 s)

Summary

Description
English: Illustration of the Heat equation.
Date
Source Own work
Author Nicoguaro
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Heat eqn.gif

Python-logo-notext.svg
This GIF graphic was created with Python.

Python

"""
Illustration of the heat equation

Solve the heat equation using finite differences and Forward Euler.

Based on: https://commons.wikimedia.org/wiki/File:Heat_eqn.gif
"""

from __future__ import division, print_function
import numpy as np
from mayavi import mlab
import subprocess

path_to_convert = "C:\Program Files\ImageMagick-6.9.3\convert.exe" 

def step_function(N, scale, X, Y, shape="crescent"):
    """Function that is 1 on a set and 0 outside of it"""
    shapes = ["crescent", "cylinder", "hexagon", "superquadric", "smiley"]
    
    if shape not in shapes:
        shape = "crescent"

    if shape == "cylinder":
        Z = np.ones_like(X)
        Z[X**2 + Y**2 < 0.5] = 0
        Z[X**2 + Y**2 > 2] = 0

    if shape == "superquadric":
        Z = np.ones_like(X)
        Z[np.abs(X)**0.5 + np.abs(Y)**0.5 > 1.5] = 0

    if shape == "hexagon":
        Z = np.ones_like(X)
        hexa = 2*np.abs(X) + np.abs(X - Y*np.sqrt(3)) +\
            np.abs(X + Y*np.sqrt(3))
        Z[hexa > 6] = 0       

    if shape == "crescent":
        c = 2
        d = -1
        e = 1
        f = 0.5
        k = 1.2
        shift = 10        
        Z = (c**2 - (X/e - d)**2 - (Y/f)**2)**2 + k*(c + d - X/e)**3 - shift
        Z = 1 - np.maximum(np.sign(Z), 0)
        
    if shape == "smiley":
        Z = np.ones_like(X)
        fac = 1.2
        x_eye = 0.5
        y_eye = 0.4
        bicorn = fac**2*(Y + 0.3)**2*(1 - fac**2*X**2) -\
                (fac**2*X**2 - 2*fac*(Y + 0.3) - 1)**2
        left_eye = (X + x_eye)**2/0.1 + (Y - y_eye)**2/0.4 - 1
        right_eye = (X - x_eye)**2/0.1 + (Y - y_eye)**2/0.4 - 1
        Z[X**2 + Y**2 > 2] = 0
        Z[bicorn > 0] = 0
        Z[left_eye < 0] = 0
        Z[right_eye < 0] = 0


    Z = scale * Z
    return Z



def data_gen(num):
    # Solve the heat equation with zero boundary conditions
    for cont in range(ntime_anim):
        Z[1:N-1, 1:N-1] = Z[1:N-1, 1:N-1] + dt*(Z[2:N, 1:N-1] +
                             Z[0:N-2, 1:N-1] + Z[1:N-1, 0:N-2] +
                             Z[1:N-1, 2:N] - 4*Z[1:N-1, 1:N-1])/dx**2

    surf = mlab.surf(X, Y, Z, colormap='autumn', warp_scale=1)
    # Change the visualization parameters.
    surf.actor.property.interpolation = 'phong'
    surf.actor.property.specular = 0.3
    surf.actor.property.specular_power = 20
    surf.module_manager.scalar_lut_manager.reverse_lut = True
    surf.module_manager.scalar_lut_manager.data_range = np.array([ 0.,  scale])

    return surf

N = 500  # Grid points
L = 2.5  # Box size
X, Y = np.mgrid[-L:L:N*1j, -L:L:N*1j]
scale = 2
Z = step_function(N, scale, X, Y, shape="crescent")
CFL = 0.125
dx = X[1, 0] - X[0, 0]
dy = dx
dt = CFL*dx**2
end_time = 0.05
time = np.arange(0, end_time, dt)
nframes = 50
ntime = time.shape[0]
ntime_anim = int(ntime/nframes)

#%% Plot frames
fname = "heat"
bgcolor = (1, 1, 1)
fig = mlab.figure(size=(1200, 1000), bgcolor=bgcolor)
fig.scene.camera.azimuth(180)
mlab.get_engine()
engine = mlab.get_engine()
scene = engine.scenes[0]
for cont in range(nframes):
    mlab.clf()
    surf = data_gen(cont)
    scene.scene.camera.position = [-8, -8,  7]
    scene.scene.camera.clipping_range = [7, 22]
    scene.scene.camera.focal_point = [0, 0, 1]
    print(cont)
    mlab.savefig("{}_{n:02d}.png".format(fname, n=cont))

#%% Generate video
args = [path_to_convert, "-delay", "10", "-loop" , "0", fname + "_*.png",
        fname + ".gif"]
subprocess.call(args, shell=True)
subprocess.call(["del", "/Q", fname + "*.png"], shell=True)
print("Done!")

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

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Date/TimeThumbnailDimensionsUserComment
current03:12, 20 May 2017Thumbnail for version as of 03:12, 20 May 20171,200 × 954 (2.66 MB)NicoguaroUser created page with UploadWizard
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