# A Fast Numerical Scheme for the Godunov-Peshkov-Romenski Model of Continuum Mechanics

## TL;DR

This paper introduces a computationally efficient second-order numerical scheme for the Godunov-Peshkov-Romenski model, balancing accuracy and speed for continuum mechanics simulations.

## Contribution

It presents a novel operator splitting scheme combining finite volume WENO reconstruction with analytic solutions for ODEs, offering a practical alternative to higher-order methods.

## Key findings

- The scheme achieves sufficient accuracy for practical purposes.
- It is computationally cheaper than existing ADER-WENO schemes.
- Convergence studies confirm the expected order of accuracy.

## Abstract

A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO reconstruction, and the temporal ODEs are solved using some analytic results presented here. Whilst it is not possible to attain arbitrary-order accuracy with this scheme (as with ADER-WENO schemes used previously), the attainable order of accuracy is often sufficient, and solutions are computationally cheap when compared with other available schemes. The new scheme is compared with an ADER-WENO scheme for various test cases, and a convergence study is undertaken to demonstrate its order of accuracy.