SEI interfacial current density calculation

[presvetli]

In sei_growth.py, I'm trying to implement calculation of SEI interfacial current density by this equation below:

I have problem with implementation, because SEI interfacial current density (j_sei) depend of same variable from previous step (j_sei). Any idea how to implement coupled_variables (j_sei) ?

[presvetli]

I tried make new variable variables["NEW SEI interfacial current density [A.m-2]"] before equation and then try update NEW variable with variables["SEI interfacial current density [A.m-2]"]

        elif self.options["SEI"] == "Degradation SEI":
            variables.update({"NEW SEI interfacial current density [A.m-2]":pybamm.Scalar(0),})
            j_sei_dim = variables["NEW SEI interfacial current density [A.m-2]"]

      .......some code.....

        # Update whole cell variables, which also updates the "sum of" variables
        variables.update(super().get_coupled_variables(variables))
        variables["NEW SEI interfacial current density [A.m-2]"] = variables["SEI interfacial current density [A.m-2]"]
        return variables

Variable variables["NEW SEI interfacial current density [A.m-2]"] is updated, but for (j_sei) equastion is used old pybamm.Scalar(0) value.

Also I tried define fundamental variable variables["NEW SEI interfacial current density [A.m-2]"] and set algebraic and initial condition,
but I got error model is overdetermined (extra algebraic keys) :

    def set_algebraic(self, variables):
        if self.options["SEI"] == ""Degradation SEI"":
            var_1 = variables["NEW SEI interfacial current density [A.m-2]"]
            self.algebraic[var_1]= variables["SEI interfacial current density [A.m-2]"]
        else:
            pass

[valentinsulzer]

Are you sure it should be i_sei and not i_tot? Usually it's i_tot in that equation. i_sei is pretty small, so i_sei * R will be too

[presvetli]

Yes, I'm sure because my R_sei is high (it is calculated by some other equation, depend on total film thickness), so i_sei*R_sei will be of the same order of magnitude as when you calculate i_tot*R.

[presvetli]

Could you please provide me some suggestions on how to solve my problem? I'm sorry, but I honestly have no idea.

[valentinsulzer]

Make i_sei a pybamm.Variable (similar to L_sei) then add an algebraic equation {i_sei: i_sei - i0_sei*exp(... - i_sei * R_sei)}

[presvetli]

Thank you for your help, it is working perfectly.