Added a video and readme.

.gitignore

@@ -0,0 +1 @@
+__pycache__

README.md

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+A finite difference code to simulate 2D advection-convection, or Rayleigh-Bernard, systems.
+Has the dependencies:
+
+1. Python 3.7
+2. Numpy
+3. SciPy
+4. Matplotlib
+
+Run the code by changing the configuration values in `main.py` and entering the following on your terminal:
+
+```
+python main.py
+```
+
+Make a video out of the results by going into the `simulations` directory and using ffmpeg like this:
+
+```
+ffmpeg -framerate 5 -pattern_type glob -i '*.png' \
+  -c:v libx264 -r 30 -pix_fmt yuv420p out.mp4
+```
+
+An example simulation with an unstable initial condition and 3:1 aspect ratio (which will favour 3 convection cells) is given below. This is the parameters currently set in `main.py`.
+
+![](example_simulation.gif)

main.py

@@ -12,11 +12,11 @@
 
 # --- Setup; using the config as a 'global variable module' --- #
 config.ny = 40
-config.nx = 80
+config.nx = 120
 config.dy = 1.0 / (config.ny)
-config.dx = 2.0 / (config.nx)
-config.dt = 0.001
-config.nt = int(0.5 / config.dt)
+config.dx = 3.0 / (config.nx)
+config.dt = 0.000125
+config.nt = int(0.2 / config.dt)
 dt = config.dt
 nt = config.nt
 ny = config.ny
@@ -159,27 +159,28 @@
             ax2.set_xlabel("t [time]")
             ax2.set_ylabel("max V [speed]")
             ax2.set_xlim([0, nt * dt])
+            ax2.set_ylim([0.01, ax2.set_ylim()[1]])
 
             # plot heat fluxes
-            ax3.plot(t[::generateEvery], heatFluxAdvectionArr)
-            ax3.plot(t[::generateEvery], heatFluxConductionArr)
-            ax3.plot(t[::generateEvery], totalHeatFluxArr, linestyle=':')
+            ax3.semilogy(t[::generateEvery], heatFluxAdvectionArr)
+            ax3.semilogy(t[::generateEvery], heatFluxConductionArr)
+            ax3.semilogy(t[::generateEvery], totalHeatFluxArr, linestyle=':')
             ax3.legend(['Advective heat flux', 'Conductive heat flux', 'Total heat flux'], fontsize=5,
-                       loc='center left')
+                       loc='lower right')
             ax3.set_xlabel("t [time]")
             ax3.set_ylabel("q [heat flux]")
             ax3.set_xlim([0, nt * dt])
             ymax = totalHeatFluxArr[0] * 1.3
-            ax3.set_ylim([0, ymax if np.max(totalHeatFluxArr) * 1.1 < ymax else np.max(totalHeatFluxArr) * 1.1])
+            ax3.set_ylim([0.01, ymax if np.max(totalHeatFluxArr) * 1.1 < ymax else np.max(totalHeatFluxArr) * 1.1])
 
             # Plot titles
             ax1.set_title("Temperature and velocity field\nstep = %i, dt = %.2e, t = %.2f" % (it, dt, t[-1] - dt),
-                          FontSize=7)
-            ax2.set_title("Maximum fluid velocity over time", FontSize=7)
-            ax3.set_title("Heat fluxes over time", FontSize=7)
+                          fontsize=7)
+            ax2.set_title("Maximum fluid velocity over time", fontsize=7)
+            ax3.set_title("Heat fluxes over time", fontsize=7)
 
             # Plot and redo!
-            plt.savefig("simulations/field%i.png" % (it / generateEvery))
+            plt.savefig("simulations/field%05i.png" % (it / generateEvery))
             clrbr.remove()
             ax1.clear()
             ax2.clear()

simulations/.gitignore

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+*.png
+