Some stand-alone functions are available in the diagnostics.py file
for computing flow diagnostics.
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).
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
\nabla\cdot\mathbf{u},
of a vector field \mathbf{u}.