Clarifying the usage of offset & LogStabilizationMoles

[ghost]

I have a few quick questions regarding the role of LogStabilizationMoles & offset.

My current understanding of the LogStabilizationMoles kernel and the offset term is: the log-molar density form in Zapdos is designed to prevent zero and negative density values. Nonetheless, for the sake of stability, an offset b is added to assist values approaching zero. This value b is added to the variable at each element, but it has the biggest impact where the variable is close to zero. Please correct me if any of this is incorrect.

Some questions following this:

1. Does the offset term strictly add some log-molar density value -b to every species variable across the whole domain? If not, what does the value b correspond to, physically speaking, or is "add" not the right word to describe its function?
2. If b indeed performs some addition function, is it only applied once, and thus its contribution is constant & uniform, or is it re-applied each timestep, like a source term with a constant rate over the whole domain?

Please correct me if I have an incorrect conception of this kernel, and thank you for your help!

[csdechant]

Your second question is on the right track. LogStabilizationMoles acts as a source term in the form of exp(-(b+u)) (please keep in mind that u here is the log form the the density, such that n = exp(u), where n is the density). Since this source term is depended on exp(-u), it will be more impactful for small densities vs large densities. There is nothing physically to b, and it is used to offset exp(-u) so that this artificial term does not full dominate the other source terms. b depends on the problem set, but we found that a b of 20 is usually sufficient. I should note that not all Zapdos simulation need this stabilization (e.g. @lindsayad and I believe @keniley1 need it for the 1D plasma-water interact simulations, but it was not required for the 1Torr argon cases I ran). I would advise trying running simulations without the stabilization, and if it seems that low densities are causing instabilities, then add LogStabilizationMoles to your simulations.

[ghost]

Thank you for confirming that I was on the right track! When I asked if b had any physical meaning, I was mostly wondering if it had some associated density value: for example, if b was 20, then it would add exp(-b) = exp(-20) = 2.061E-9 mol/m^3 to each point where u exists. Looking at how its formulated, exp(-(b+u)) it looks like it would exponentially increase the addition as b + u further drops below 0, add little to nothing if b + u = 0 or greater. A higher b value would then suggest it lets u decrease farther before acting as a significant source.

Is there some density n that is just too low for Zapdos to handle, thus requiring the use of LogStabilizationMoles? My first guess is that in the plasma-liquid sims, some species' densities may go below this threshold at some point, but in the argon sims the density never goes below the threshold so you don't need the offset. Or is this picture too simplistic?

[csdechant]

For your first statement, I am not sure if assigning b as some density value was the original vision for this stabilization method, but one could see it as such. Let n_b be a density value, such that n_b = exp(-b) if a positive b value, then LogStabilizationMoles is define as n_b*exp(-u) or n_b / n. So when n ≥ n_b, then the artificial source term is 1 or less and when n < n_b, then the artificial source term is greater then 1. So, in terms of b, a larger b results in a smaller n_b. This means the artificial source term is 1 or less for a greater range of n densities. (So yes, that was a round about way of agreeing with your statement of "A higher b value would then suggest it lets u decrease farther before acting as a significant source")

As for a "threshold", the species' densities are not the dominating factor. It is the energy density (i.e. n_ε = ε * n_e, where n_ε is the energy density, ε is the electron mean energy, and n_e is the electron density). For the plasma-water simulations, the electron energy drops nearly to zero at the plasma-liquid interface, causing the instability. In the low pressure argon simulations, the electron energy is never that low. As for a limit of how low the electron energy can be before causing instabilities, I have study how the electron energy affects simulation results, but I have yet to set a "hard" limit to that.

[ghost]

Oh! The electron energy causes instabilities, not species' densities? That is very useful to know... Thank you for the golden nugget of knowledge and your help clarifying the kernel!