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

1998; Elsevier BV; Volume: 151; Issue: 1-2 Linguagem: Inglês

10.1016/s0045-7825(97)00119-9

1879-2138

Eugenio Oñate,

Numerical methods for differential equations

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.