A Q-SCHEME FOR A CLASS OF SYSTEMS OF COUPLED CONSERVATION LAWS WITH SOURCE TERM. APPLICATION TO A TWO-LAYER 1-D SHALLOW WATER SYSTEM

By M. Castro, J. Macías, C. Parés. 2001

175 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/cea5584a0b85cb8640f48c084b5c0749cc3057b9

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, methodology): “Among those we note the work in [27] using an upwind scheme for single layer shallow water, and [7 ]w here the two-layer shallow water system is solved using the Q-scheme [ 6 ], the scheme in [8,28], based on a CWENO reconstruction, and the relaxation scheme for two-layer shallow-water presented in ”
On the well-balance property of Roe?s method for nonconservative hyperbolic systems (2004, methodology): “The bilayer shallow water system We consider in this paragraph the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids studied in [4]:  ∂h1 ∂t + ∂q1 ∂x = 0,”
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods (2008, unknown): “Roe method was studied in [4] and [9], a family of numerical schemes, including numerical schemes using flux-limiters, was studied in [13].”
A robust well-balanced scheme for multi-layer shallow water equations (2010, methodology): “We can observe that this property (28) is true for Roe type solvers like those of [4], [9], because in this context the source discretization can be chosen arbitrarily.”
Numerical methods for nonconservative hyperbolic systems: a theoretical framework (2006, background): “preserve some equilibria: see [2], [3], [5], [7], [10], [11], [12], [17], [18], [23], [24], [27], [29], [31], [32], [36], [37], [38], [39], .”