Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

By Sebastian Noelle, Normann Pankratz, Gabriella Puppo, Jostein R. Natvig. Journal of Computational Physics, 2006

340 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/af2a6daa8542a57dc55a631d54ac48a89eb25255

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In Computational Mechanics

Citations in the corpus

A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, neutral): “Higher order ENO/WENO based algorithms are given in [8,28] and more recently in [19,20] using the equilibrium variables Q and E.”
Tsunami modelling with adaptively refined finite volume methods* (2011, background): “Okada (1992), ‘Internal deformation due to shear and tensile faults in a halfspace’, Bull.”
A new model of granular flows over general topography with erosion and deposition (2008, background): “People use well-balanced schemes to obtain the steady state even when there is a singularity caused by Coulomb friction, namely u=juj at u ¼ 0, e.g., [35], [ 36 ].”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, methodology): “The methods that exactly preserve such solutions are called well-balanced, and we refer the reader to [2, 4, 8, 10, 12, 16, 17, 20, 21, 22, 23, 27, 28], where a variety of highorder well-balanced schemes for the Saint-Venant system can be found.”
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, positive): “Remark 4.3: Audusse et al. [1] introduced a second order well balanced finite volume scheme, and recently, Noelle et al. [ 21 ] generalized it to higher order accuracy.”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Using the idea of extrapolation [39, 40], we can extend the source term approximation to any order of accuracy.”
High-order balanced CWENO scheme for movable bed shallow water equations (2007, neutral): “[24].”
Godunov-type methods for free-surface shallow flows: A review (2007, methodology): “These schemes are applicable to the shallow water type equations, see Crnjaric-Zic et al., (2004), Noelle et al. (2006) and Xing and Shu (2005).”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, methodology): “, [41] for an example with FV methods and §5.”
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].”