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A fast numerical scheme for the Godunov-Peshkov-Romenski model of continuum mechanics

Published version
Peer-reviewed

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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.

Description

Keywords

Godunov–Peshkov–Romenski, GPR, continuum mechanics, operator splitting, ADER, WENO

Journal Title

Journal of Computational Physics

Conference Name

Journal ISSN

0021-9991
1090-2716

Volume Title

348

Publisher

Elsevier
Sponsorship
Engineering and Physical Sciences Research Council (EP/L015552/1)
I acknowledge financial support from the EPSRC Centre for Doctoral Training in Computational Methods for Materials Science under grant EP/L015552/1.