# The Godunov Method for a 2-Phase Model

## TL;DR

This paper applies the Godunov numerical method to a phase-transition traffic model, demonstrating its effectiveness through numerical tests and comparing it with a different existing model.

## Contribution

It introduces the application of the Godunov method to a specific phase-transition traffic model and analyzes its differences with another established model.

## Key findings

- Numerical tests confirm the validity of the Godunov method for this model.
- The paper highlights key differences between the proposed model and an alternative model.
- The method effectively captures phase transitions in traffic flow.

## Abstract

We consider the Godunov numerical method to the phase-transition traffic model, proposed in [6], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [1], by Blandin, Work, Goatin, Piccoli, and Bayen.