The notion of conservation for residual distribution schemes (or fluctuation splitting schemes), with some applications
This is a review paper that provides a unified perspective on conservation for residual distribution schemes, which is of interest to researchers in computational fluid dynamics and numerical methods for hyperbolic PDEs.
The paper discusses discrete conservation for hyperbolic conservation laws, introducing fluctuation splitting schemes and showing that most known schemes can be rephrased in flux form while satisfying additional conservation laws.
In this paper, we discuss the notion of discrete conservation for hyperbolic conservation laws. We introduce what we call a fluctuation splitting schemes (or residual distribution, also RDS) and show on several examples how this cal lead to new development. In particular, we show that most, if not all known schemes can be rephrased in flux form, and also show how to satisfy additional conservation laws. This review paper is built on \cite{AbgrallConservation,Abgrall2017,paola,svetlana,ABGRALL2018640}.