A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservati

By Laurent Gosse. 2001

155 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/9a32076a32b6c0477609f262c144197cea8ae46f

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Numerical methods for nonconservative hyperbolic systems: a theoretical framework (2006, unknown): “preserve some equilibria: see [2], [3], [5], [7], [10], [11], [12], [17], [18], [23], [24], [27], [29], [31], [32], [36], [37], [38], [39], .”
CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM (2002, background): “For other related works on balance laws we refer to [6, 13,16,35].”
A kinetic scheme for the Saint-Venant system¶with a source term (2001, unknown): “…[10],[11] introduced the notion of well-balanced scheme and they use a reformulation of the source terms by means of non-conservative products to derive their numerical ﬂuxes; this kind of numerical processing has been recently extended by Gosse [12],[13] to hyperbolic systems of balance laws.”
An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations (2002, background): “…(cid:2)x stand for the piecewise constant functions coinciding with u ,v the appropriate (cid:2) (cid:2)x , there holds for all t > 0 and 1 (cid:2) p (cid:2) +∞ : and the scheme (6) is positivity-preserving If moreover u 0 ,v 0 BV ( R ) , under the same conditions, one has (cid:11) (cid:11)”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “Numerical treatment of the friction term is made by using the approach of Gosse [16,17], which leads to the following system of governing equations:”
Godunov method for nonconservative hyperbolic systems (2007, methodology): “Some results of convergence for Godunov methods applied to systems of balance laws can be found in [14] or [9].”
Tsunami modelling with adaptively refined finite volume methods* (2011, methodology): “L. Gosse (2001), ‘A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms’, Math.”
Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws (2003, background): “Quite recently, these kinds of numerical processing have been extended to hyperbolic systems of balance laws (like the Saint-Venant system for shallow waters), to obtain stable schemes which preserve the steady states (see [8], [13],[14] and [28], for instance).”
Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations (2004, methodology): “By combining the well-balanced schemes that were initially introduced by Greenberg and LeRoux in the scalar case [14] and later by Gosse for the balance laws systems [12], with some approximate Riemann solvers, Gallou€et et al.”