My question is regarding solving the conservative form and the non-conservative form of the governing-equations (GE), like continuity or the navier stokes equation, using finite difference method (FDM) and finite volume method (FVM).
When reading about the differences between the conservative form and the non-conservative forms of the GE it was said that since in the conservative form the dependent variables are the fluxes (and not the primitive variables) they are better conserved and "physically" correct. (among other things)
When reading about the differences between the FDM and FVM it was said that the finite volume was better at conserving the fluxes which are an advantage. (among other things)
Here are my questions:
When using FVM do we only solve equations in conservative form?
When solving the conservative form of the GE using FDM are the fluxes conserved or does this only apply when solving the equations using FVM.
If we solve the GE in the conservative form using FDM and then using FVM what will be the difference? ie will the "conservativeness" be the same for both FDM and FVM methods?