A Roe-type scheme for two-phase shallow granular flows over variable topography

Marica Pelanti; François Bouchut; Anne Mangeney

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 5, page 851-885
  • ISSN: 0764-583X

Abstract

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We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid components, coupled together by both conservative and non-conservative terms involving the derivatives of the unknowns, and by interphase drag source terms. The system is hyperbolic at least when the difference between solid and fluid velocities is sufficiently small. We solve numerically the one-dimensional model equations by a high-resolution finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution. We present and discuss several numerical experiments, including problems of perturbed steady flows over non-flat bottom surface that show the efficient modeling of disturbances of equilibrium conditions.

How to cite

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Pelanti, Marica, Bouchut, François, and Mangeney, Anne. "A Roe-type scheme for two-phase shallow granular flows over variable topography." ESAIM: Mathematical Modelling and Numerical Analysis 42.5 (2008): 851-885. <http://eudml.org/doc/250336>.

@article{Pelanti2008,
abstract = { We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid components, coupled together by both conservative and non-conservative terms involving the derivatives of the unknowns, and by interphase drag source terms. The system is hyperbolic at least when the difference between solid and fluid velocities is sufficiently small. We solve numerically the one-dimensional model equations by a high-resolution finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution. We present and discuss several numerical experiments, including problems of perturbed steady flows over non-flat bottom surface that show the efficient modeling of disturbances of equilibrium conditions. },
author = {Pelanti, Marica, Bouchut, François, Mangeney, Anne},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Granular flows; two-phase flows; thin layer approximation; non-conservative systems; numerical model; finite volume schemes; Riemann solvers; well-balanced schemes.; granular flows; non-conservative systems; Riemann solvers; well-balanced schemes},
language = {eng},
month = {7},
number = {5},
pages = {851-885},
publisher = {EDP Sciences},
title = {A Roe-type scheme for two-phase shallow granular flows over variable topography},
url = {http://eudml.org/doc/250336},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Pelanti, Marica
AU - Bouchut, François
AU - Mangeney, Anne
TI - A Roe-type scheme for two-phase shallow granular flows over variable topography
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/7//
PB - EDP Sciences
VL - 42
IS - 5
SP - 851
EP - 885
AB - We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid components, coupled together by both conservative and non-conservative terms involving the derivatives of the unknowns, and by interphase drag source terms. The system is hyperbolic at least when the difference between solid and fluid velocities is sufficiently small. We solve numerically the one-dimensional model equations by a high-resolution finite volume scheme based on a Roe-type Riemann solver. Well-balancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution. We present and discuss several numerical experiments, including problems of perturbed steady flows over non-flat bottom surface that show the efficient modeling of disturbances of equilibrium conditions.
LA - eng
KW - Granular flows; two-phase flows; thin layer approximation; non-conservative systems; numerical model; finite volume schemes; Riemann solvers; well-balanced schemes.; granular flows; non-conservative systems; Riemann solvers; well-balanced schemes
UR - http://eudml.org/doc/250336
ER -

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