Journal of Computational Physics
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Upwinding of the source term at interfaces for Euler equations with high friction
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Comparison between discrete and continuum modeling of granular spreading
MATH'06 Proceedings of the 10th WSEAS International Conference on APPLIED MATHEMATICS
Conservative arbitrary order finite difference schemes for shallow-water flows
Journal of Computational and Applied Mathematics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
Conservative discretization of Coriolis force in a finite volume framework
Journal of Computational Physics
Computers & Mathematics with Applications
A positive MUSCL-Hancock scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Scientific Computing
A simple finite volume method for the shallow water equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Numerical approximation for a Baer-Nunziato model of two-phase flows
Applied Numerical Mathematics
Finite volume schemes for dispersive wave propagation and runup
Journal of Computational Physics
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
SIAM Journal on Numerical Analysis
A fast adaptive quadtree scheme for a two-layer shallow water model
Journal of Computational Physics
Journal of Computational Physics
Shallow Water Flows in Channels
Journal of Scientific Computing
Journal of Scientific Computing
Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green---Naghdi Model
Journal of Scientific Computing
Journal of Scientific Computing
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms
Journal of Scientific Computing
Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying
Journal of Scientific Computing
A numerical treatment of wet/dry zones in well-balanced hybrid schemes for shallow water flow
Applied Numerical Mathematics
Analysis of a new Kolgan-type scheme motivated by the shallow water equations
Applied Numerical Mathematics
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations
Journal of Computational Physics
Asymptotic High Order Mass-Preserving Schemes for a Hyperbolic Model of Chemotaxis
SIAM Journal on Numerical Analysis
On the well-balanced numerical discretization of shallow water equations on unstructured meshes
Journal of Computational Physics
High Order Well-Balanced WENO Scheme for the Gas Dynamics Equations Under Gravitational Fields
Journal of Scientific Computing
Journal of Computational Physics
A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations
Journal of Scientific Computing
The Journal of Supercomputing
Journal of Computational Physics
Well-Balanced Adaptive Mesh Refinement for shallow water flows
Journal of Computational Physics
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We consider the Saint-Venant system for shallow water flows, with nonflat bottom. It is a hyperbolic system of conservation laws that approximately describes various geophysical flows, such as rivers, coastal areas, and oceans when completed with a Coriolis term, or granular flows when completed with friction. Numerical approximate solutions to this system may be generated using conservative finite volume methods, which are known to properly handle shocks and contact discontinuities. However, in general these schemes are known to be quite inaccurate for near steady states, as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions. This difficulty can be overcome by using the so-called well-balanced schemes. We describe a general strategy, based on a local hydrostatic reconstruction, that allows us to derive a well-balanced scheme from any given numerical flux for the homogeneous problem. Whenever the initial solver satisfies some classical stability properties, it yields a simple and fast well-balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality.