A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions

By Derek S. Bale, Randall J. LeVeque, Sorin Mitran, James A. Rossmanith. SIAM Journal on Scientific Computing, 2002

326 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/b34890bd851467a606bac5c488ca825064436b1c

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows (2006, background): “Closely related schemes usually try to discretize the derivative of the convective flux and the source term by one and the same finite difference or finite volume operator, see [2,4,29].”
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.”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “A quasi-steady wave propagation algorithm based on modified Riemann problems is presented in [2, 33, 34].”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, unknown): “Key-words: Shallow water equations, finite volume schemes, well-balanced schemes Mathematics Subject Classification: 65M12, 76M12, 35L65”
A New Approach of High Order Well-Balanced Finite Volume WENO Schemes and Discontinuous Galerkin Methods for a Class of Hyperbolic Systems with Source Terms (2006, unknown): “1 Elastic wave equation We consider the propagation of compressional waves [2, 30] in an one-dimensional elastic rod with a given media density ρ(x).”
Tsunami modelling with adaptively refined finite volume methods* (2011, unknown): “See also Bale et al. (2002), Gosse (2001, 2000) and In (1999).”
Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations (2004, methodology): “In [1], the extension of the wave propagation algorithm to the hyperbolic conservation and balance laws with spatially varying flux functions was considered.”
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms (2006, methodology): “Next, we present the numerical result for a linear acoustic test [1].”