# On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network

## TL;DR

This paper validates a finite volume numerical scheme with monotone transmission conditions for scalar conservation laws on star-shaped networks by comparing with explicit solutions and Riemann problem solutions, supporting its accuracy and applicability.

## Contribution

It provides the first validation of a finite volume scheme with monotone transmission conditions for networked scalar conservation laws through explicit and Riemann problem comparisons.

## Key findings

- Scheme accurately reproduces explicit solutions
- Effective in solving Riemann problems on networks
- Supports further validation of the finite volume method

## Abstract

In this paper we validate the implementation of the numerical scheme proposed in [3]. The validation is made by comparison with an explicit solution here obtained, and the solutions of Riemann problems for several networks. We then perform some simulations in order to qualitatively validate the model under consideration. Such results represent also a first step for the validation of the finite volumes scheme introduced in [9].