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<br />
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.