Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources

By François Bouchut. 2005

767 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/4aa7bf2e1a5aedf066ad5821297b6ce117951088

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods (2008, unknown): “See [50], [4], [26], [27], [40], [22], [23], [46], [9], [56], [47], [12], [13], [3], [6], [43].”
Tsunami modelling with adaptively refined finite volume methods* (2011, background): “As mentioned above, this has led to the development of well-balanced schemes for such systems (see e.g. Bale, LeVeque, Mitran and Rossmanith (2002), Bouchut (2004), George (2008), Greenberg and LeRoux (1996), Botta, Klein, Langenberg and Lützenkirchen (2004), Gallardo, Parés and Castro (2007),…”
Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, background): “An example of a Cauchy problem when h D 0 is the Riemann problem for genuinely discontinuous initial datum (see for instance [6, 23]).”
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], .”
On the use of Saint Venant equations to simulate the spreading of a granular mass (2005, methodology): “Friction as an Apparent Topography [25] The apparent topography method is general and can be used to deal with generic source terms [see Bouchut, 2004].”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, methodology): “A generalization to the case of the Saint-Venant system was obtained in [28], and another method by relaxation is also proposed in [7].”
Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help (2011, background): “Indeed, the time step, for a constant mesh size ∆x, has to satisfy the so called Courant-FriedichsLewy condition (CFL condition) in what follows, (see [10], [11] and references therein) (17) |λmax|∆t < ∆x where |λmax| is the maximum of the modulus of the eigenvalues or in other words, λmax is the ma”