Piacsek, S. A., and G. P. Williams, 1970: Conservation properties convection difference schemes. Journal of Computational Physics, 6, 392-405.

Abstract: The so-called conservative or flux form of the finite difference formulation of convection terms is shown to be inadequate for preventing nonlinear instability in some cases. A preferred scheme for the convection terms which has the property of absolute spatial conservation is obtained. Illustrative examples are given for (i) the Navier-Stokes equations; (ii) a forced convection equation; and (iii) a Burger's type equation.