A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids

Sébastien Boyaval (1, 2)

1 LHSV - Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics
2 MATHERIALS - MATHematics for MatERIALS

Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Upper-Convected Maxwell (UCM) fluids was proposed in [Bouchut & Boyaval, 2013], which preserved a physically-natural stability property (i.e. free-energy dissipation) of the full system. It invoked a relaxation scheme of Suliciu type for the numerical computation of approximate solution to Riemann problems. Here, the approach is extended to the 1D Saint-Venant system generalized to the finitely-extensible nonlinear elastic fluids of Peterlin (FENE-P). We are currently not able to ensure all stability conditions a priori, but numerical simulations went smoothly in a practically useful range of parameters.

Mots clés: Finite-Volume; Saint-Venant equations; 35Q30; Suliciu relaxation scheme; MSC (2010): 65M08; simple Riemann solver; 65N08; FENE-P viscoelastic fluids

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

Sébastien Boyaval. A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids. Clément Cancès; Pascal Omnes. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, 200, Springer, pp.163-170, 2017, Print ISBN : 978-3-319-57393-9 / online : 978-3-319-57394-6. ⟨10.1007/978-3-319-57394-6_18⟩. ⟨hal-01433712⟩