Discretization of the viscous dissipation term with the MAC scheme
Résumé
We propose a discretization for the MAC scheme of the viscous dissipation term τ (u) : ∇u (where τ (u) stands for the shear stress tensor associated to the velocity field u), which is suitable for the approximation of this term in a conservation equation for a scalar variable. This discretization enjoys the property that the integral over the computational domain Ω of the (discrete) dissipation term is equal to what is obtained when taking the inner product of the (discrete) momentum balance equation by u and integrating over Ω. As a consequence, it may be used as an ingredient to obtain an unconditionally stable scheme for the compressible Navier-Stokes equations. It is also shown, in some model cases, to ensure the strong convergence in L1 of the dissipation term.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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