A fast numerical scheme for the Godunov-Peshkov-Romenski model of continuum mechanics
Published version
Peer-reviewed
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Type
Article
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Authors
Jackson, Haran https://orcid.org/0000-0002-5731-6888
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
1090-2716
Volume Title
348
Publisher
Elsevier
Publisher DOI
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.