A simple fully well-balanced and entropy preserving scheme for the shallow-water equations

DOI10.1016/j.aml.2018.07.013zbMath1410.65338OpenAlexW2809669506WikidataQ129470859 ScholiaQ129470859MaRDI QIDQ1726473

Christophe Berthon, Victor Michel-Dansac

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.07.013

zbMATH Keywords

shallow-water equationswell-balanced schemesGodunov-type schemesmoving steady statesentropy-satisfying schemes

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (3)

A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms ⋮ A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction ⋮ Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws

Uses Software

• HLLE
• HE-E1GODF

Cites Work

• Unnamed Item
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• A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
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• A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations
• Riemann Solvers and Numerical Methods for Fluid Dynamics
• On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
• Simplified Godunov Schemes for $2 \times 2$ Systems of Conservation Laws
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows

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