How to define the pseudo-time step limit?

[pohlan]

• For the diffusion part of ϕ, we use the CFL criterion, what about the other terms including vo, vc, m? This would especially be relevant for h, there we only use a randomly determined scalar for all grid points at the moment.

• What should be the relation to dt, the physical time step? min(CFL, dt), a harmonic mean or something else?

[pohlan]

Experimenting with the numerical parameters showed that dτ_h (pseudo-time step for h) cannot be chosen completely randomly. If it is too large, ϕ has problems to converge, and if it is too small h and also ϕ converge very slowly. Furthermore it seems to depend on the grid resolution. I tried making it somehow proportional to Res_h, Res_ϕ or dτ_ϕ but couldn't figure out anything useful. I only managed to get the expected model output for a constant dτ_h determined through try and error.

[mauro3]

dh/dt is the recation-part of the \phi equation. Is there something about how to choose a time step for a reaction-diffusion equation?

[pohlan]

But h is not just a reaction of ϕ diffusion, it influences the diffusion itself (with the factor h^α in the effective diffusivity). Possibly that's a reason why the h pseudo-time step is limited somehow. In this specific case, the h values mostly increase over pseudo-time, so if h advances quickly the effective diffusivity is very large, such that ϕ can only take tiny steps and doesn't converge well. This would fit together with the observation that ϕ generally converges better for small dτ_h, but then h itself converges very slowly and if dτ_h is too small the error just produces NaNs. Anyway, this is just some guessing, the issue might as well be somewhere else. But what I don't quite understand is why it doesn't work well if ϕ and h have the same pseudo-time step.

[mauro3]

oo small the error just produces NaNs

Why is that?

dh/dt = vo-vc and vo-vc features as reaction term. Hmm, but you're right, it probably does not matter.