A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations

2015/02/25 by Christophe Berthon, Christophe Chalons · 71 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Applied mathematics #Computational Fluid Dynamics and Aerodynamics #Entropy (arrow of time) #Geology #Godunov's scheme #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Numerical analysis #Shallow water equations #Thermodynamics #Type (biology) #Work (physics)

paper · doi:10.1090/mcom3045

published in Mathematics of Computation 85(299), 1281-1307 (American Mathematical Society)

openalex publication_date 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26

Abstract

This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-known shallow-water model. During the last two decades, several well-balanced strategies have been introduced with special attention to the exact capture of the stationary states associated with the so-called lake at rest. By fully well-balanced, we mean here that the proposed Godunov-type method is also able to preserve stationary states with non zero velocity. The numerical procedure is shown to preserve the positiveness of the water height and satisfies a discrete entropy inequality.

Citations

• Hyperbolic systems of conservation laws II

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• A well-balanced reconstruction with bounded velocities for the shallow water equations by convex combination
• A large time-step and well-balanced Lagrange-Projection type scheme for\n the shallow-water equations

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