Consistency and stability are two essential ingredients in the design of
numerical algorithms for partial differential equations. Robust algorithms can
be developed by incorporating nonlinear physical stability principles in their
design, such as the entropy production inequality (c'est-à-dire, the Clausius-Duhem
inequality or second law of thermodynamics), rather than by simply adding
artificial viscosity (a common approach). This idea is applied to the k-epsilon
and two-equation turbulence models by introducing space-time averaging. Then, a
set of entropy variables can be defined which leads to a symmetric system of
advective-diffusive equations. Positivity and symmetry of the equations require
certain constraints on the turbulence diffusivity coefficients and the
turbulence source terms. With these, we are able to design entropy producing
two-equation turbulence models and, en particulier, the k-epsilon model.

Cet article explore les excursions dans le temps et leurs implications.

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