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Communication Dans Un Congrès Année : 2011

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.
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hal-00576268 , version 1 (13-08-2011)

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Fabrice Babik, Raphaele Herbin, Walid Kheriji, Jean-Claude Latché. Discretization of the viscous dissipation term with the MAC scheme. FVCA 6, Internal Symposium, Jun 2011, Prague, Czech Republic. pp.571-579, ⟨10.1007/978-3-642-20671-9_60⟩. ⟨hal-00576268⟩
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