How come Finite Volume Method(FVM) handle the unstructured meshes and Finite difference Method cannot, whereas in FVM to approximate the fluxes at the boundary we use the central differencing?
My understanding is that in FDM, to apply Taylor series, we need lines on which other independent variables are constant (as on x-axis, y=z=0). Whereas in the case of FVM, to calculate the boundary fluxes we are actually doing interpolation between two points, which do not pose any such restriction of constant lines. In the case of uniform orthogonal meshes, the usual interpolation turns out to be the central difference approximation.
Is my understanding correct? If not, please help me clarify this misconception.