Source code for pybamm.models.submodels.electrode.ohm.composite_ohm

#
# Composite model for Ohm's law in the electrode
#
import pybamm

from .base_ohm import BaseModel




class Composite(BaseModel):
    """An explicit composite leading and first order solution to solid phase
    current conservation with ohm's law. Note that the returned current density is
    only the leading order approximation.

    Parameters
    ----------
    param : parameter class
        The parameters to use for this submodel
    domain : str
        Either 'Negative electrode' or 'Positive electrode'
    options : dict, optional
        A dictionary of options to be passed to the model.
    """

    def __init__(self, param, domain, options=None):
        super().__init__(param, domain, options=options)



    def get_coupled_variables(self, variables):
        domain = self.domain

        i_boundary_cc = variables["Current collector current density [A.m-2]"]

        # import parameters and spatial variables
        L_n = self.param.n.L
        L_p = self.param.p.L
        L_x = self.param.L_x
        x_n = pybamm.standard_spatial_vars.x_n
        x_p = pybamm.standard_spatial_vars.x_p

        tor = variables[f"X-averaged {domain} electrode transport efficiency"]
        phi_s_cn = variables["Negative current collector potential [V]"]
        T = variables[f"X-averaged {domain} electrode temperature [K]"]

        sigma_eff = self.domain_param.sigma(T) * tor
        if self._domain == "negative":
            phi_s = phi_s_cn + (i_boundary_cc / sigma_eff) * (
                x_n * (x_n - 2 * L_n) / (2 * L_n)
            )
            i_s = i_boundary_cc * (1 - x_n / L_n)

        elif self.domain == "positive":
            delta_phi_p_av = variables[
                "X-averaged positive electrode surface potential difference [V]"
            ]
            phi_e_p_av = variables["X-averaged positive electrolyte potential [V]"]

            const = (
                delta_phi_p_av
                + phi_e_p_av
                + (i_boundary_cc / sigma_eff) * (L_x - L_p / 3)
            )

            phi_s = const - (i_boundary_cc / sigma_eff) * (
                x_p + (x_p - L_x) ** 2 / (2 * L_p)
            )
            i_s = i_boundary_cc * (1 - (L_x - x_p) / L_p)

        variables.update(self._get_standard_potential_variables(phi_s))
        variables.update(self._get_standard_current_variables(i_s))

        if self.domain == "positive":
            variables.update(self._get_standard_whole_cell_variables(variables))

        return variables




    def set_boundary_conditions(self, variables):
        domain, Domain = self.domain_Domain

        phi_s = variables[f"{Domain} electrode potential [V]"]
        tor = variables[f"X-averaged {domain} electrode transport efficiency"]
        i_boundary_cc = variables["Current collector current density [A.m-2]"]
        T = variables[f"X-averaged {domain} electrode temperature [K]"]

        if self.domain == "negative":
            lbc = (pybamm.Scalar(0), "Dirichlet")
            rbc = (pybamm.Scalar(0), "Neumann")

        elif self.domain == "positive":
            lbc = (pybamm.Scalar(0), "Neumann")
            sigma_eff = self.param.p.sigma(T) * tor
            rbc = (-i_boundary_cc / sigma_eff, "Neumann")

        self.boundary_conditions[phi_s] = {"left": lbc, "right": rbc}