The numerical simulation for Kelvin-Helmholtz instability is quite challenging. To verify the accuracy of our method, we compare the temperature and the vorticity at time t=6 on a y=0.5 cut between two resolutions: 2048 X 256, 4096 X 512.

The following picture shows the comparison of temperature profile. The solid line represents the result computed by the resolution 4096 X 512, while the star line represents that of 2048 X 256. To make the plot clearly, we only plot the even points in the start line. In other words, the graph of the star line only shows 1025 points.

Accordingly, the comparison between the two resolutions for the vorticity with the same horizontal line and time is shown below:

It is evident that even though there are so many rolling up structures and sharp transitional areas for temperature and vorticity profiles, the results using two resolutions match perfectly well.