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

Published in Comput. Methods Appl. Mech. Engrg., Vol. 151 (1-2), pp. 233-265, 1998
doi: 10.1016/S0045-7825(97)00119-9

Abstract

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 reinterprete many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter.