Kinetic Schemes for Saint-Venant Equations with Source Terms on Unstructured Grids

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Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method (2003, methodology): “In [1] only the homogeneous Saint-Venant system has a kinetic interpretation and the source terms are upwind at the macroscopic level.”
Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme (2003, unknown): “Furthermore, it is proved that the water height positivity is preserved under the Courant Friedrichs Levy condition [ Audusse et al. , 2000] (cid:4) t max [ 22 ] In comparison with flood modeling, avalanche modeling introduces a further difficulty relating to the property of granular media able to…”
The generalized Riemann problem method for the shallow water equations with bottom topography (2006, background): “In recent years the numerical treatment of (1) has attracted much attention, leading to a variety of schemes, see References [3–18] and references therein.”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, methodology): “Following [1], [5], [6], we propose and analyze finite volume schemes according to (2.”
A kinetic scheme for the Saint-Venant system¶with a source term (2001, unknown): “Implementation in two spatial dimensions is also in progress (see [1] for a first attempt).”