# Flux-conservative Hermite methods for simulation of nonlinear conservation laws

## TL;DR

This paper introduces a novel class of Hermite methods for nonlinear conservation laws that maintain high-order accuracy and enhanced stability, incorporating entropy viscosity to effectively capture shocks.

## Contribution

The paper presents a new Hermite method class that improves stability and shock capturing in nonlinear conservation law simulations.

## Key findings

- Achieves high-order accuracy for smooth solutions.
- Enhanced stability properties over existing methods.
- Effective shock capturing using entropy viscosity.

## Abstract

A new class of Hermite methods for solving nonlinear conservation laws is presented. While preserving the high order spatial accuracy for smooth solutions in the existing Hermite methods, the new methods come with better stability properties. Artificial viscosity in the form of the entropy viscosity method is added to capture shocks.