Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems

The concept of the so-called 'artificial or balancing diffusion' used to stabilize the numerical solution of advective-diffusive transport and fluid flow problems is revised in this paper. it is shown that the standard forms of the balancing diffusion terms,, usually chosen in a heuristic manner, can be naturally found by introducing higher-order approximations in the derivation of the governing differential equations via standard conservation (or equilibrium) principles. This allows us to reinterpret many stabilization algorithms and concepts used in every-day practice by numerical analysts and also provides an expression for computing the stabilization parameter.