Unified formal reduction for fluid models of free-surface shallow gravity-flows

François Bouchut (1) , Sébastien Boyaval (2, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LHSV - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics
3 MICMAC - Methods and engineering of multiscale computing from atom to continuum

We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence property that univoquely defines one reduced model given one rheology and one thin-layer regime. For the first time, as far as we know, various known reduced models can thus be investigated within a single mathematical framework, for various rheologies (viscous and viscoelastic) and various limit regimes (fast inertial flows and slow viscous flows). Furthermore, our systematic procedure also produces new reduced models for viscoelastic non-Newtonian fluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8, 2013].

Mots clés: viscoelastic fluids; non-Newtonian fluids; lubrication model; shallow-water model; model reduction; gravity-flows; thin-layer fluids

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

François Bouchut, Sébastien Boyaval. Unified formal reduction for fluid models of free-surface shallow gravity-flows. 2013. ⟨hal-00833468v1⟩