ENO and WENO Schemes with the Exact Conservation Property for One-Dimensional Shallow Water Equations

By S. Vukovic, Luka Sopta. 2002

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/1718e33b894452dc026ae87487d63df37d9ceebb

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, background): “High order finite difference and finite volume WENO schemes which are well balanced for the still water solution of the shallow water equations, and a more general class of balance laws, were designed in [117, 168, 171, 172, 173, 174].”
Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations (2004, methodology): “First higher order schemes that respect balancing between the source term and the flux gradient, which is crucial for preserving some steady state solutions were developed in [27].”
High-order balanced CWENO scheme for movable bed shallow water equations (2007, methodology): “A recent work by Vuković and Sopta [36], in a ENO-WENO framework, exactly satisfies the C-property, but the complexity of its method is relevant.”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, background): “Though the exact solution of this initial-boundary value problem is not available, it seems to be a generic problem for accuracy tests since most known solutions (in closed form) have special properties making the leading term in truncation errors in many schemes vanish (see [26, 27]).”
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms (2006, methodology): “Different from [33,34], a key ingredient of the technique used in [35] is a special decomposition of the source term, allowing a discretization to the source term to be both high order accurate for general solutions and exactly well balanced with the flux gradient for still water.”