A note on the central-upwind scheme for nonlocal conservation laws
Abstract
The central-upwind flux is a widely used numerical flux function for local conservation laws. It has been investigated by Kurganov and Polizzi (2009) for a specific nonlocal conservation law and can be derived from a fully-discrete second-order scheme. Here, we derive this fully-discrete scheme in detail with a particular focus on the occurring nonlocal terms. In addition, we derive the central-upwind flux for a class of nonlocal conservation laws and use an estimate on the nonlocal speed which fixes the nonlocality at the cell interfaces. We prove that the resulting first-order numerical scheme converges to the correct solution. Under additional assumptions on the analytical flux we present a similar result for a second-order central-upwind scheme. Numerical examples compare the central-upwind schemes to Godunov-type schemes and the fully-discrete scheme.
Cite
@article{arxiv.2512.01344,
title = {A note on the central-upwind scheme for nonlocal conservation laws},
author = {Jan Friedrich and Samala Rathan and Sanjibanee Sudha},
journal= {arXiv preprint arXiv:2512.01344},
year = {2026}
}