Hyperbolic balance laws: residual distribution, local and global fluxes

Remi Abgrall (1, 2) , Mario Ricchiuto (2)

1 UZH - Universität Zürich [Zürich] = University of Zurich
2 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

This review paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux [61] 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.

Domaines: Modélisation et simulation

Remi Abgrall, Mario Ricchiuto. Hyperbolic balance laws: residual distribution, local and global fluxes. 2021. ⟨hal-03508452v2⟩