Linear interpolation formula seems funky for fvm - am I interpreting correctly?

[jelc53]

I would have thought we would try to estimate surface concentration by 'adding' our linear gradient step to the fN (concentration value at final cell interior node). Am I interpreting this correctly for 'right' boundary and 'linear' extrapolation ?

Code here (formula in comment of line 914): https://github.com/pybamm-team/PyBaMM/blob/develop/pybamm/spatial_methods/finite_volume.py#L813

[jelc53]

FWIW, I think it should be f(x*) = f_N + (dxN / dxNm1) (f_N - f_Nm1) instead of # f(x*) = f_N - (dxN / dxNm1) (f_N - f_Nm1). I think that is how it is implemented in the CSR matrix code.

[valentinsulzer]

This

csr_matrix(
                            (
                                [-(dxN / dxNm1), 1 + (dxN / dxNm1)],
                                ([0, 0], [prim_pts - 2, prim_pts - 1]),
                            ),
                            shape=(1, prim_pts),
                        )

is f_N + (dxN/dxNm1) * (f_N-f_Nm1)

[jelc53]

Oh so there is a typo in the comment then! It says f(x*) = f_N - (dxN / dxNm1) (f_N - f_Nm1) when it should be f(x*) = f_N + (dxN/dxNm1) * (f_N-f_Nm1) as you say (minus flips to plus). This makes sense to me since it would be logically equivalent to the neumann boundary (use_bcs) version above in the code (f(x*) = f_N + dxN * f'(x*)).