Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

DOI10.1137/17M1152887zbMath1403.35224OpenAlexW2785500639MaRDI QIDQ4684191

Emmanuel Audusse, Nina Aguillon, Edwige Godlewski, Martin Parisot

Publication date: 27 September 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1152887

zbMATH Keywords

shallow water equationsRiemann problemhyperbolic conservation lawsnonconservative productscoalescence of waveslayerwise discretization

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) Shock waves and blast waves in fluid mechanics (76L05) Free-surface potential flows for incompressible inviscid fluids (76B07) First-order hyperbolic systems (35L40) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

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Uses Software

• HE-E1GODF

Cites Work

• Unnamed Item
• Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model: kinetic interpretation and numerical solution
• A multilayer Saint-Venant model: derivation and numerical validation
• A simple 1D model of inviscid fluid-solid interaction
• Analysis and computation with stratified fluid models
• Layer-averaged Euler and Navier-Stokes equations
• Multi-dimensional shear shallow water flows: problems and solutions
• The Riemann problem for a class of resonant hyperbolic systems of balance laws
• Numerical approximation of hyperbolic systems of conservation laws
• Definition and weak stability of nonconservative products
• Analytical solutions for the free surface hydrostatic Euler equations
• A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation
• Asymptotic Shallow Water Models for Internal Waves in a Two-Fluid System with a Free Surface
• A new model of roll waves: comparison with Brock’s experiments
• Local Well-Posedness of the Two-Layer Shallow Water Model with Free Surface
• Fully nonlinear long-wave models in the presence of vorticity
• Finite Volume Methods for Hyperbolic Problems
• Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law
• Riemann problem for a particle–fluid coupling
• Gas-dynamic analogy for vortex free-boundary flows