Question on the DFN surface formulation model equations

Hi Everyone,

This is just a question about the model equations for the ‘surface formulation’ of the DFN model.

I am running some simple simulations to compare this formulation with other model types. I was just curious about the exact PDE formulation of the model. Could someone point me to a paper/reference that has the exact PDE form for this model? I tried looking through the docs but couldn’t find a reference for it. My code for this is at the bottom of this message.

Thanks so much!

Tosh

%%

import matplotlib.pyplot as plt
import numpy as np
import pybamm

Code to run full order dfn

parameter_values = pybamm.ParameterValues(“Marquis2019”)

options = {“thermal”: “isothermal”}
model = pybamm.lithium_ion.DFN(options)

experiment = pybamm.Experiment(
[
“Discharge at 1C for 1 hours or until 2.8 V”,
“Charge at 1C until 4.1 V”,
]
)

safe_solver = pybamm.CasadiSolver(atol=1e-6, rtol=1e-6, mode=“safe”,return_solution_if_failed_early=True,dt_max=None)

sim = pybamm.Simulation(model, experiment=experiment,parameter_values=parameter_values,solver=safe_solver)

solution = sim.solve()

t = solution[“Time [s]”]
time_vector_full = t.entries
V = solution[“Voltage [V]”]
V_cell_full = V.entries

%%

Code to run surface formulation dfn

import matplotlib.pyplot as plt
import numpy as np
import pybamm

Code to run surface formulation of DFN model

parameter_values = pybamm.ParameterValues(“Marquis2019”)
model =pybamm.lithium_ion.DFN(options={“surface form”: “differential”}, name=“DFN”)
experiment = pybamm.Experiment(
[
“Discharge at 1C for 1 hours or until 2.8 V”,
“Charge at 1C until 4.1 V”,
]
)

safe_solver = pybamm.ScipySolver(atol=1e-12)

sim = pybamm.Simulation(model, experiment=experiment,parameter_values=parameter_values,solver=safe_solver)

solution = sim.solve()

t = solution[“Time [s]”]
time_vector_surf = t.entries
V = solution[“Voltage [V]”]
V_cell_surf = V.entries

%%

Code for plotting

plt.figure(1)
plt.plot(time_vector_full,V_cell_full,‘r-’,label = “Full Order DFN”)
plt.plot(time_vector_surf,V_cell_surf,‘b–’,label = “Surface Form DFN”)
plt.legend(loc=“upper left”)
plt.xlabel(“Time [s]”)
plt.ylabel(“Cell Voltage [v]”)
plt.grid()
plt.show()