Is the Poisson's equation really solved in IonFreeFlame?

[Akira Shioyoke]

Dear all,

I'm trying to know the effect of external electric field on flame propagation.
I understand that main branch of Cantera can't solve external electric field, but can solve ion distribution and internal electric field.

However, I found diag was set as 0 in IonFlow::evalResidual fundion.
(https://github.com/Cantera/cantera/blob/main/src/oneD/IonFlow.cpp#L211)
As I understood, diag = 0 means the residual is not contributed when solving equations in Newton method, and was neglected.

I also checked residual of eField using Sim1D::saveResidual function.
Residual of eField is in a order of 1e0.
So, I wonder Poisson's equation is not solved in IonFreeFlame example.

My question is

    Is the Poisson's equation really solved in IonFreeFlame?
    If above question is yes, how eField was calculated and what does it mean physicaly?

Thank you

Akira.

[Bang-Shiuh Chen]

Hello Akira,

diag = 0 means that this equation is not time dependent (there is no time term in the Poisson's equation). I believe that there are some other properties that also have diag = 0. You can check StFlow. Some explanation is provided at https://www.et.byu.edu/~tom/classes/641/Cantera/Workshop/flames.pdf. You can compare the solution of StFlow (regular) and IonFlow. I recently pushed a PR on github, https://github.com/Cantera/cantera-website/pull/167. Once it get approved, you will see the equations. Since now only internal electric field is solved, we do not need full Poisson's equation, instead Gauss's law is used to solve electric field. See section of Differential form at https://en.wikipedia.org/wiki/Gauss%27s_law. BTW, Moses from NC state university is working with me on improving this feature so that we can add external voltage. If you are interested in this, you are welcome to join us.

Best,

Bang