Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system

DOI10.1090/mcom/3099zbMath1416.65386arXiv1409.3825OpenAlexW2322861651WikidataQ57964526 ScholiaQ57964526MaRDI QIDQ5741493

Marie-Odile Bristeau, Jacques Sainte-Marie, Emmanuel Audusse, François Bouchut

Publication date: 25 July 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3825

zbMATH Keywords

shallow water equationswell-balanced schemeshydrostatic reconstructionkinetic solverfully discrete entropy inequality

Mathematics Subject Classification ID

Particle methods and lattice-gas methods (76M28) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods applied to problems in solid mechanics (74S10) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (9)

Well-Balanced Second-Order Finite Element Approximation of the Shallow Water Equations with Friction ⋮ A multi well-balanced scheme for the shallow water MHD system with topography ⋮ Entropy stable flux correction for hydrostatic reconstruction scheme for shallow water flows ⋮ Convergence of finite volume schemes for the Euler equations via dissipative measure-valued solutions ⋮ Numerical approximation of the 3D hydrostatic Navier–Stokes system with free surface ⋮ Improvement of the hydrostatic reconstruction scheme to get fully discrete entropy inequalities ⋮ Convergence of the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography ⋮ Surface reconstruction schemes for shallow water equations with a nonconservative product source term ⋮ Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

Cites Work

• Unnamed Item
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• Numerical simulations of a non-hydrostatic shallow water model
• Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model: kinetic interpretation and numerical solution
• A robust well-balanced scheme for multi-layer shallow water equations
• Construction of BGK models with a family of kinetic entropies for a given system of conservation laws
• Entropy satisfying flux vector splittings and kinetic BGK models
• Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws
• A well-balanced positivity preserving ``second-order scheme for shallow water flows on unstructured meshes
• A kinetic scheme for the Saint-Venant system with a source term
• High-order well-balanced finite volume WENO schemes for shallow water equation with moving water
• Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy
• A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
• A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows
• A kinetic interpretation of the section-averaged Saint-Venant system for natural river hydraulics
• Boltzmann Type Schemes for Gas Dynamics and the Entropy Property
• WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE
• Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Computing Qualitatively Correct Approximations of Balance Laws
• A Survey of High Order Schemes for the Shallow Water Equations
• A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles
• Numerical Passage from Kinetic to Fluid Equations

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