Source code for pybamm.models.submodels.electrolyte_diffusion.full_diffusion

#
# Class for electrolyte diffusion employing stefan-maxwell
#
import numpy as np

import pybamm

from .base_electrolyte_diffusion import BaseElectrolyteDiffusion




class Full(BaseElectrolyteDiffusion):
    """Class for conservation of mass in the electrolyte employing the
    Stefan-Maxwell constitutive equations. (Full refers to unreduced by
    asymptotic methods)

    Parameters
    ----------
    param : parameter class
        The parameters to use for this submodel
    options : dict, optional
        A dictionary of options to be passed to the model.
    """

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



    def get_fundamental_variables(self):
        eps_c_e_dict = {}
        for domain in self.options.whole_cell_domains:
            Domain = domain.capitalize()
            eps_c_e_k = pybamm.Variable(
                f"{Domain} porosity times concentration [mol.m-3]",
                domain=domain,
                auxiliary_domains={"secondary": "current collector"},
                bounds=(0, np.inf),
                scale=self.param.c_e_init_av,
            )
            eps_c_e_k.print_name = f"eps_c_e_{domain[0]}"
            eps_c_e_dict[domain] = eps_c_e_k

        variables = self._get_standard_porosity_times_concentration_variables(
            eps_c_e_dict
        )

        return variables




    def get_coupled_variables(self, variables):
        c_e_dict = {}
        for domain in self.options.whole_cell_domains:
            Domain = domain.capitalize()
            eps_k = variables[f"{Domain} porosity"]
            eps_c_e_k = variables[f"{Domain} porosity times concentration [mol.m-3]"]
            c_e_k = eps_c_e_k / eps_k
            c_e_dict[domain] = c_e_k

        variables["Electrolyte concentration concatenation [mol.m-3]"] = (
            pybamm.concatenation(*c_e_dict.values())
        )
        variables.update(self._get_standard_domain_concentration_variables(c_e_dict))

        c_e = (
            variables["Porosity times concentration [mol.m-3]"] / variables["Porosity"]
        )
        variables.update(self._get_standard_whole_cell_concentration_variables(c_e))

        # Whole domain
        tor = variables["Electrolyte transport efficiency"]
        i_e = variables["Electrolyte current density [A.m-2]"]
        v_box = variables["Volume-averaged velocity [m.s-1]"]
        T = variables["Cell temperature [K]"]

        N_e_diffusion = -tor * self.param.D_e(c_e, T) * pybamm.grad(c_e)
        N_e_migration = self.param.t_plus(c_e, T) * i_e / self.param.F
        N_e_convection = c_e * v_box

        N_e = N_e_diffusion + N_e_migration + N_e_convection

        variables.update(self._get_standard_flux_variables(N_e))
        variables.update(
            {
                "Electrolyte diffusion flux [mol.m-2.s-1]": N_e_diffusion,
                "Electrolyte migration flux [mol.m-2.s-1]": N_e_migration,
                "Electrolyte convection flux [mol.m-2.s-1]": N_e_convection,
            }
        )

        return variables




    def set_rhs(self, variables):
        eps_c_e = variables["Porosity times concentration [mol.m-3]"]
        c_e = variables["Electrolyte concentration [mol.m-3]"]
        N_e = variables["Electrolyte flux [mol.m-2.s-1]"]
        div_Vbox = variables["Transverse volume-averaged acceleration [m.s-2]"]

        sum_s_a_j = variables["Sum of electrolyte reaction source terms [A.m-3]"]
        sum_s_a_j.print_name = "aj"
        source_terms = sum_s_a_j / self.param.F

        self.rhs = {eps_c_e: -pybamm.div(N_e) + source_terms - c_e * div_Vbox}




    def set_initial_conditions(self, variables):
        eps_c_e = variables["Porosity times concentration [mol.m-3]"]

        self.initial_conditions = {
            eps_c_e: self.param.epsilon_init * self.param.c_e_init
        }




    def set_boundary_conditions(self, variables):
        c_e = variables["Electrolyte concentration [mol.m-3]"]
        c_e_conc = variables["Electrolyte concentration concatenation [mol.m-3]"]
        T = variables["Cell temperature [K]"]
        tor = variables["Electrolyte transport efficiency"]
        i_boundary_cc = variables["Current collector current density [A.m-2]"]

        def flux_bc(side):
            # returns the flux at a separator/electrode interface
            # assuming v_box = 0 for now
            return (
                pybamm.boundary_value(
                    -(1 - self.param.t_plus(c_e, T))
                    / (tor * self.param.D_e(c_e, T) * self.param.F),
                    side,
                )
                * i_boundary_cc
            )

        if self.options.whole_cell_domains[0] == "negative electrode":
            # left bc at anode/current collector interface
            lbc = pybamm.Scalar(0)
        elif self.options.whole_cell_domains[0] == "separator":
            # left bc at anode/separator interface
            lbc = flux_bc("left")
        if self.options.whole_cell_domains[-1] == "positive electrode":
            # right bc at cathode/current collector interface
            rbc = pybamm.Scalar(0)
        # elif self.options.whole_cell_domains[-1] == "separator":
        #     # right bc at separator/cathode interface
        #     rbc = flux_bc("right")

        # add boundary conditions to both forms of the concentration
        self.boundary_conditions = {
            c_e: {"left": (lbc, "Neumann"), "right": (rbc, "Neumann")},
            c_e_conc: {"left": (lbc, "Neumann"), "right": (rbc, "Neumann")},
        }