Numerical methods for nonconservative hyperbolic systems: a theoretical framework

By Carlos Parés Madroñal. SIAM Journal on Numerical Analysis, 2006

350 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/c205b75d0343ac5cc217fafaf6acf9390f88791f

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Godunov-type methods for free-surface shallow flows: A review (2007, methodology): “Recent advances regarding non-conservative systems and numerical methods have been reported by Pares and collaborators (Castro et al., 2006a, b; Pares, 2006).”
Well-Balanced High-Order Centred Schemes for Non-Conservative Hyperbolic Systems. Applications to Shallow Water Equations with Fixed and Mobile Bed (2009, methodology): “Moreover, based on the theoretical advances in [9], generalizations of the Roe method to systems of the form (1) have been introduced in [33,5,26].”
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws (2011, methodology): “3) which makes it very similar to the Roe method [35], that can be also defined in a weak, integral manner according to [5, 32, 48] and that with the use of the segment path (3.”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Path-conservative methods for the non-conservative product are introduced in [13, 42] and extended to the SWEs.”
FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems (2010, methodology): “(31) Following [28], we define the numerical flux as Gi+ 1 2 = G(W−h ,W+h , n) := F (W−h ) · n + D−(W−h ,W+h , n), (32) where simple algebraic manipulations reveal that Gi+ 1 2 satisfies the usual consistency requirements.”
Godunov method for nonconservative hyperbolic systems (2007, methodology): “Consistency of Godunov method for weak solutions In [20] a Lax-Wendroff type result was conjectured for path-conservative numerical schemes: if the approximations provided by a path-conservative scheme converge to some function as the mesh is refined, then this function should be a weak solution of ”