2021/09/17 by Rémi Abgrall, Abgrall, Remi, Mario Ricchiuto +1 · 1 citation
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2109.08491
openalex publication_date 2021/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux in fluctuation form. The so-called multidimensional fluctuation schemes have historically first been developed for steady homogeneous hyperbolic systems. Their application to unsteady problems and conservation laws has been really understood only relatively recently. This understanding has allowed to make of the residual distribution framework a powerful playground to develop numerical discretizations embedding some prescribed constraints. This paper describes in some detail these techniques, with several examples, ranging from the compressible Euler equations to the Shallow Water equations.