The main idea behind the Finite Volume Method FVM is that what goes in must

come out and vice-versa.

If the domain is divided into a number of volumes, areas for 2D or lines for

1D, which are bounded by surfaces, lines in 2D and points in 1D, that are shared

between pairs of such sub volumes, then it is obvious that if something leaves

one volume through a shared surface then what just left will have gone into the

neighbor volume through that same shared surface.

The exception to this is the outer boundaries which are not shared between sub

volumes, but only belongs to one volume. At the boundaries, there need to be

boundary conditions as usual.

The full text is in the form of a PDF document that can be downloaded at the bottom of this page.