I am currently trying to solve some PDEs with FiPy. At page 56, the manual mentions (https://www.ctcms.nist.gov/fipy/download/fipy-3.0.pdf).
The largest stable timestep that can be taken for this explicit 1D diffusion problem is $∆t ≤ ∆x^ 2/(2D)$.
A few questions that might appear basic but I'm having a really hard time getting my head around:
Why is that inequality? How does that scale for 2D and 3D problems?
Shouldn't units come into play here? For example, if I converted by time-step from hours to minutes, then clearly the magnitude of the value would change, even though the actual time represented would remain the same? Or does the fact I am also scaling the Diffusivity (which depends both on the units of space and time) ensures the inequality remains sound?