[Bug]: Variable equality is not preserved at domain interphase

[DundalekJan]

PyBaMM Version

25.4.2

Python Version

3.9.13

Describe the bug

I am observing that the variable equality (electrolyte potential and electrolyte concentration) is not preserved at domain interphase within solver tolerances. I use in my simulations default numbers of points with default relative and absolute solver tolerances.

Steps to Reproduce

import pybamm

model = pybamm.lithium_ion.DFN()
parameter_values=pybamm.ParameterValues('Chen2020')

experiment = pybamm.Experiment(['Discharge at 1C for 30 minutes'])
sim = pybamm.Simulation(model=model, parameter_values=parameter_values, experiment=experiment)
sim.solve()
sol=sim.solution

t_sample=max(sol.t)
x_bns=parameter_values['Negative electrode thickness [m]']
x_bsp=parameter_values['Negative electrode thickness [m]']+parameter_values['Separator thickness [m]']
print('Electrolyte potential at negative electrode-separator boundary')
phi_e_bns=sol['Electrolyte potential [V]'](t=t_sample,x=x_bns)
print(' - "Negative electrolyte potential" vs "Electrolyte potential"')
phi_ne_bns=sol['Negative electrolyte potential [V]'](t=t_sample,x=x_bns)
print('   - absolute deviation [V]: '+str(phi_ne_bns-phi_e_bns))
print('   - relative deviation [-]: '+str((phi_ne_bns-phi_e_bns)/phi_e_bns))
print(' - "Separator electrolyte potential" vs "Electrolyte potential"')
phi_se_bns=sol['Separator electrolyte potential [V]'](t=t_sample,x=x_bns)
print('   - absolute deviation [V]: '+str(phi_se_bns-phi_e_bns))
print('   - relative deviation [-]: '+str((phi_se_bns-phi_e_bns)/phi_e_bns))
print('')
print('Electrolyte potential at separator-positive electrode boundary')
phi_e_bsp=sol['Electrolyte potential [V]'](t=t_sample,x=x_bsp)
print(' - "Separator electrolyte potential" vs "Electrolyte potential"')
phi_se_bsp=sol['Separator electrolyte potential [V]'](t=t_sample,x=x_bsp)
print('   - absolute deviation [V]: '+str(phi_se_bsp-phi_e_bsp))
print('   - relative deviation [-]: '+str((phi_se_bsp-phi_e_bsp)/phi_e_bsp))
print(' - "Positive electrolyte potential" vs "Electrolyte potential"')
phi_pe_bsp=sol['Positive electrolyte potential [V]'](t=t_sample,x=x_bsp)
print('   - absolute deviation [V]: '+str(phi_pe_bsp-phi_e_bsp))
print('   - relative deviation [-]: '+str((phi_pe_bsp-phi_e_bsp)/phi_e_bsp))
print('')
print('')
print('Electrolyte concentration at negative electrode-separator boundary')
c_e_bns=sol['Electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bns)
print(' - "Negative electrolyte concentration" vs "Electrolyte concentration"')
c_ne_bns=sol['Negative electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bns)
print('   - absolute deviation [mol.m-3]: '+str(c_ne_bns-c_e_bns))
print('   - relative deviation [-]: '+str((c_ne_bns-c_e_bns)/c_e_bns))
print(' - "Separator electrolyte concentration" vs "Electrolyte concentration"')
phi_se_bns=sol['Separator electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bns)
print('   - absolute deviation [mol.m-3]: '+str(phi_se_bns-c_e_bns))
print('   - relative deviation [-]: '+str((phi_se_bns-c_e_bns)/c_e_bns))
print('')
print('Electrolyte concentration at separator-positive electrode boundary')
c_e_bsp=sol['Electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bsp)
print(' - "Separator electrolyte concentration" vs "Electrolyte concentration"')
c_se_bsp=sol['Separator electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bsp)
print('   - absolute deviation [mol.m-3]: '+str(c_se_bsp-c_e_bsp))
print('   - relative deviation [-]: '+str((c_se_bsp-c_e_bsp)/c_e_bsp))
print(' - "Positive electrolyte concentration" vs "Electrolyte concentration"')
c_pe_bsp=sol['Positive electrolyte concentration [mol.m-3]'](t=t_sample,x=x_bsp)
print('   - absolute deviation [mol.m-3]: '+str(c_pe_bsp-c_e_bsp))
print('   - relative deviation [-]: '+str((c_pe_bsp-c_e_bsp)/c_e_bsp))

Relevant log output

Electrolyte potential at negative electrode-separator boundary
 - "Negative electrolyte potential" vs "Electrolyte potential"
   - absolute deviation [V]: -0.00036311572573907713
   - relative deviation [-]: 0.0015423251629823785
 - "Separator electrolyte potential" vs "Electrolyte potential"
   - absolute deviation [V]: -0.0001231738798248283
   - relative deviation [-]: 0.0005231780416266227

Electrolyte potential at separator-positive electrode boundary
 - "Separator electrolyte potential" vs "Electrolyte potential"
   - absolute deviation [V]: 5.413445853100218e-05
   - relative deviation [-]: -0.00022512061117577144
 - "Positive electrolyte potential" vs "Electrolyte potential"
   - absolute deviation [V]: 0.00010668551351444844
   - relative deviation [-]: -0.00044365656658816187


Electrolyte concentration at negative electrode-separator boundary
 - "Negative electrolyte concentration" vs "Electrolyte concentration"
   - absolute deviation [mol.m-3]: -1.8603160897802127
   - relative deviation [-]: -0.0021204991088142047
 - "Separator electrolyte concentration" vs "Electrolyte concentration"
   - absolute deviation [mol.m-3]: -2.4816230159749466
   - relative deviation [-]: -0.0028287017581025203

Electrolyte concentration at separator-positive electrode boundary
 - "Separator electrolyte concentration" vs "Electrolyte concentration"
   - absolute deviation [mol.m-3]: 0.8463012480577845
   - relative deviation [-]: 0.0010459294281669775
 - "Positive electrolyte concentration" vs "Electrolyte concentration"
   - absolute deviation [mol.m-3]: -0.24807998109781693
   - relative deviation [-]: -0.0003065978614173066