# 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

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topPelanti, 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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