An upwind vertex centred finite volume algorithm for nearly and truly incompressible explicit fast solid dynamic applications: Total and Updated Lagrangian formulations

Hassan, O. I., Ghavamian, A., Lee, C. H. , Gil, A. J., Bonet, J. and Auricchio, F. (2019) An upwind vertex centred finite volume algorithm for nearly and truly incompressible explicit fast solid dynamic applications: Total and Updated Lagrangian formulations. Journal of Computational Physics: X, 3, 100025. (doi: 10.1016/j.jcpx.2019.100025)

Abstract

This paper presents an explicit vertex centred finite volume method for the solution of fast transient isothermal large strain solid dynamics via a system of first order hyperbolic conservation laws. Building upon previous work developed by the authors, in the context of alternative numerical discretisations, this paper explores the use of a series of enhancements (both from the formulation and numerical standpoints) in order to explore some limiting scenarios, such as the consideration of near and true incompressibility. Both Total and Updated Lagrangian formulations are presented and compared at the discrete level, where very small differences between both descriptions are observed due to the excellent discrete satisfaction of the involutions. In addition, a matrix-free tailor-made artificial compressibility algorithm is discussed and combined with an angular momentum projection algorithm. A wide spectrum of numerical examples is thoroughly examined. The scheme shows excellent (stable, consistent and accurate) behaviour, in comparison with other methodologies, in compressible, nearly incompressible and truly incompressible bending dominated scenarios, yielding equal second order of convergence for velocities, deviatoric and volumetric components of the stress.

• Item Type: Articles
• Additional Information: The authors gratefully acknowledge the financial support provided by the Sêr Cymru National Research Network for Advanced Engineering and Materials (Grant No. G05), United Kingdom. The first and second authors would also like to acknowledge the financial support received through the European Commission EACEA Agency, Framework Partnership Agreement 2013-0043 Erasmus Mundus Action 1b, as a part of the EM Joint Doctorate “Simulation in Engineering and Entrepreneurship Development (SEED)”.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lee, Dr Chun Hean
• Authors: Hassan, O. I., Ghavamian, A., Lee, C. H., Gil, A. J., Bonet, J., and Auricchio, F.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Journal of Computational Physics: X
• Publisher: Elsevier
• ISSN: 2590-0552
• ISSN (Online): 2590-0552
• Published Online: 24 May 2019
• Copyright Holders: Copyright © 2019 Elsevier Inc.
• First Published: First published in Journal of Computational Physics: X 3:100025
• Publisher Policy: Reproduced under a Creative Commons License