I have come across the paper titled:A monolithic fluid structure interaction algorithm ... For a 1D grid, at the boundaries the paper uses virtual nodes $x_{0}$ and $x_{N+1}$ (page 372)and for instance for velocity v at the boundaries ends up via extrapolation with (page 374)$x_{0} = 2 x_{1}-x_{2}$and $x_{N+1} = 2 x_{N}-x_{N-1}$I was wondering if someone could explain to me where the points N and 0 lie? On the faces or at nodes? Also what is the reason for using this extrapolation. Thank you! 
FVM - virtual node discretisation
finite volume;discretization;hyperbolic pde;extrapolation