TY - GEN
T1 - A finite-volume discretization of viscoelastic saint-venant equations for FENE-P fluids
AU - Boyaval, Sébastien
N1 - Publisher Copyright:
© Springer International Publishing AG 2017.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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 and Boyaval (M3AS 23(08): 1479–1526, 2013, [6]), 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 solutions 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 the scheme is fully computable. And, using numerical simulations, it may help understand the famous High-Weissenberg number problem (HWNP) well-known in computational rheology.
AB - 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 and Boyaval (M3AS 23(08): 1479–1526, 2013, [6]), 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 solutions 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 the scheme is fully computable. And, using numerical simulations, it may help understand the famous High-Weissenberg number problem (HWNP) well-known in computational rheology.
KW - Fene-p viscoelastic fluids
KW - Finite-volume
KW - Saint-venant equations
KW - Simple riemann solver
KW - Suliciu relaxation scheme
UR - https://www.scopus.com/pages/publications/85020402965
U2 - 10.1007/978-3-319-57394-6_18
DO - 10.1007/978-3-319-57394-6_18
M3 - Conference contribution
AN - SCOPUS:85020402965
SN - 9783319573939
T3 - Springer Proceedings in Mathematics and Statistics
SP - 163
EP - 170
BT - Finite Volumes for Complex Applications VIII— Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017
A2 - Omnes, Pascal
A2 - Cances, Clement
PB - Springer New York LLC
T2 - 8th International Symposium on Finite Volumes for Complex Applications - Hyperbolic, Elliptic and Parabolic Problems, FVCA8 2017
Y2 - 12 June 2017 through 16 June 2017
ER -