Not converging into steady-state solution directly

[pohlan]

Even for the SHMIP "sqrt" geometry, the physical time steps dt cannot be larger than ~ 1000 seconds. Therefore the steady-state can only be reached after many physical time steps. The goal would be to do only one large time step and reach steady-state directly.

[pohlan]

@luraess What do you say to the new definition of dtau? Why do we need the dt? The fact that dτ_h was proportional to dt caused domain errors for large dts, which is why it was not possible to reach steady-state in one time step.

https://github.com/pohlan/SheetModel.jl/blob/0e5775fb5c0ccd28f71a53fc174d1b1ac2265e61/src/SheetModel.jl#L384-L388

Now the physical time step dt can be arbitrarily large.

[luraess]

@luraess What do you say to the new definition of dtau? Why do we need the dt?

If it works better as such - go for it 👍 .

From other experience, if you have a time-dependent diffusion equation and take small steps, then the code may diverge if the physical dt does not show up in the iterative dtau definition. Since we target the steady-state in one time step, dt (large) may no longer me an issue and one can certainly drop it from the dtau definition. I'll think more about it.