Generating Animation with a Constant Scale Colormap

How to generate an animation with a constant scale for the colormap?

When the colorbar scale (min-max) changes as the solution progresses, the reason can be found in the settings of the contour plots.

Open the contour plot settings, deselect the Auto Range option (and Clip to Range if not needed) and enter the range minimum and maximum values for the variable you want to plot.