A unified surface-gradient and hydrostatic reconstruction scheme for the shallow water equations

Journal of Computational Physics, vol. 467, pp. 111463

DOI: 10.1016/j.jcp.2022.111463 OpenAlex

Authors 2

Guoxian Chen corresponding

Wuhan University

Affiliation as printed

Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, PR China

School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, PR China
Sebastian Noelle Aachen Institute for Geometry and Practical Mathematics

RWTH Aachen University

Affiliation as printed

Institute for Geometry and Practical Mathematics, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

Cited by 11 stored of 11

Well-balanced finite difference WENO schemes for shallow water equations with constant subtraction technique
2026 Computers & Mathematics with Applications article Engineering Computational Fluid Dynamics and Aerodynamics Open access

0

citations
Well-Balanced Fifth-Order Moment-Based Hermite WENO Schemes for Shallow Water Equations in New Pre-Balanced Form
2026 Communications in Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

0

citations
The Generalized Riemann Problem for Two-Layer Shallow Water Equations with Two-Velocities
2025 Advances in Applied Mathematics and Mechanics article Mathematics Differential Equations and Numerical Methods

0

citations
Invariant Region Preserving Reconstruction and Enhanced Stability of the Central Scheme in Two Dimensions
2025 Journal of Computational Mathematics article Physics and Astronomy Quantum chaos and dynamical systems

0

citations
Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models
2025 Applied Numerical Mathematics article Engineering Computational Fluid Dynamics and Aerodynamics

1

citations
Well-Balanced Fifth-Order Finite Volume WENO Schemes with Constant Subtraction Technique for Shallow Water Equations
2025 Journal of Scientific Computing article Engineering Computational Fluid Dynamics and Aerodynamics

3

citations
A positivity-preserving well-balanced wet-dry front reconstruction for shallow water equations on rectangular grids
2024 Applied Numerical Mathematics article Engineering Computational Fluid Dynamics and Aerodynamics

5

citations
A well-balanced positivity-preserving multidimensional central scheme for shallow water equations
2023 Applied Numerical Mathematics article Engineering Computational Fluid Dynamics and Aerodynamics

3

citations
A 3rd/2nd order MOOD limited scheme for the shallow water equations
2023 PAMM article Engineering Computational Fluid Dynamics and Aerodynamics Open access

0

citations
A mass conservative, well balanced and positivity-preserving central scheme for shallow water equations
2022 Applied Mathematics and Computation article Engineering Computational Fluid Dynamics and Aerodynamics

8

citations
An efficient invariant-region-preserving central scheme for hyperbolic conservation laws
2022 Applied Mathematics and Computation article Engineering Computational Fluid Dynamics and Aerodynamics

11

citations

11 results

No patents citing this paper on Lens.org (checked 2026-10-06).

References 38

Shock-Capturing Methods for Free-Surface Shallow Flows
2001 Institutional Research Information System (Università degli Studi di Trento) book Engineering Computational Fluid Dynamics and Aerodynamics

1,232

citations
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
2004 SIAM Journal on Scientific Computing article Engineering Computational Fluid Dynamics and Aerodynamics

1,028

citations
On Godunov-type methods near low densities
1991 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

1,001

citations
Definition and weak stability of nonconservative products
1995 OpenGrey (Institut de l'Information Scientifique et Technique) article Engineering Control and Stability of Dynamical Systems

720

citations
A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
1996 SIAM Journal on Numerical Analysis article Engineering Computational Fluid Dynamics and Aerodynamics

686

citations
The Surface Gradient Method for the Treatment of Source Terms in the Shallow-Water Equations
2001 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

558

citations
Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources
2004 Medical Entomology and Zoology book Engineering Computational Fluid Dynamics and Aerodynamics

535

citations
Numerical resolution of well-balanced shallow water equations with complex source terms
2009 Advances in Water Resources article Engineering Computational Fluid Dynamics and Aerodynamics

526

citations
A high‐resolution Godunov‐type scheme in finite volumes for the 2D shallow‐water equations
1993 International Journal for Numerical Methods in Fluids article Engineering Computational Fluid Dynamics and Aerodynamics

464

citations
Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations
2011 WORLD SCIENTIFIC eBooks book Engineering Computational Fluid Dynamics and Aerodynamics

452

citations
A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
2007 Communications in Mathematical Sciences article Engineering Computational Fluid Dynamics and Aerodynamics Open access

441

citations
Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation
2001 Discrete and Continuous Dynamical Systems - B article Mathematics Navier-Stokes equation solutions

385

citations
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
2010 Advances in Water Resources article Engineering Computational Fluid Dynamics and Aerodynamics

352

citations
Central-Upwind Schemes for the Saint-Venant System
2002 ESAIM Mathematical Modelling and Numerical Analysis article Engineering Computational Fluid Dynamics and Aerodynamics Open access

324

citations
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
2005 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

314

citations
High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems
2006 Mathematics of Computation article Engineering Computational Fluid Dynamics and Aerodynamics Open access

294

citations
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions
2003 SIAM Journal on Scientific Computing article Engineering Computational Fluid Dynamics and Aerodynamics

283

citations
High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
2007 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

269

citations
Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes
2008 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics Open access

250

citations
On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas
2007 Journal of Computational Physics article Engineering Computational Fluid Dynamics and Aerodynamics

220

citations