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.
Keywords: granular flows, two-phase flows, thin layer approximation, non-conservative systems, numerical model, finite volume schemes, Riemann solvers, well-balanced schemes
@article{M2AN_2008__42_5_851_0, author = {Pelanti, Marica and Bouchut, Fran\c{c}ois and Mangeney, Anne}, title = {A {Roe-type} scheme for two-phase shallow granular flows over variable topography}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {851--885}, publisher = {EDP-Sciences}, volume = {42}, number = {5}, year = {2008}, doi = {10.1051/m2an:2008029}, mrnumber = {2454625}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008029/} }
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: Modélisation mathématique et analyse numérique PY - 2008 SP - 851 EP - 885 VL - 42 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008029/ DO - 10.1051/m2an:2008029 LA - en ID - M2AN_2008__42_5_851_0 ER -
%0 Journal Article %A Pelanti, Marica %A Bouchut, François %A Mangeney, Anne %T A Roe-type scheme for two-phase shallow granular flows over variable topography %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 851-885 %V 42 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008029/ %R 10.1051/m2an:2008029 %G en %F M2AN_2008__42_5_851_0
Pelanti, Marica; Bouchut, François; Mangeney, Anne. A Roe-type scheme for two-phase shallow granular flows over variable topography. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 5, pp. 851-885. doi : 10.1051/m2an:2008029. http://www.numdam.org/articles/10.1051/m2an:2008029/
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