Add functionality for analyzing and calculating statistics on physical quantity gradients when computing Euler equations

For the analysis functionality, the implementation related to physical quantity gradients can only be realized when parabolic terms are present. When calculating the Euler equations, gradient statistics cannot be computed.

The issue mentions existing analysis functionality for physical quantity gradients and Euler-equation computations, but names no files or tests. Start by locating the gradient-statistics implementation and an Euler-equation analysis entry point; done means gradient statistics can be computed for Euler equations as well as cases with parabolic terms.

Written by the indexing model from the issue text.