Diagnostic fields

Some stand-alone functions are available in the diagnostics.py file for computing flow diagnostics.

Courant number

The Courant number diagnostic computes the field defined by

\[\frac{||\mathbf{u}||\Delta t}{\Delta x},\]

where \(\Delta t\) is the time-step size and \(\Delta x\) is the element size (more specifically, it is twice the element’s circumradius).

Grid Reynolds number

The Reynolds number (whose length scale is relative to the element size \(\Delta x\)) is defined by

\[\mathrm{Re} = \frac{\rho||\mathbf{u}||\Delta x}{\mu},\]

where \(\rho\) is the fluid density, \(\mu\) is the dynamic viscosity, and \(||\mathbf{u}||\) is the magnitude to the velocity field. Alternatively,

\[\mathrm{Re} = \frac{||\mathbf{u}||\Delta x}{\nu},\]

where \(\nu\) is the kinematic viscosity.


This diagnostic field computes the divergence


of a vector field \(\mathbf{u}\).