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

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

Hassan, Osama I., Ghavamian, Ataollah, Lee, Chun Hean ORCID: 0000-0003-1102-3729, Gil, Antonio J., Bonet, Javier ORCID: 0000-0002-0430-5181 and Auricchio, Ferdinando (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. ISSN 2590-0552 (doi:https://doi.org/10.1016/j.jcpx.2019.100025)

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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: Article
Uncontrolled Keywords: Conservation laws, solid dynamics, Lagrangian, FVM, upwind, JST
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 15 Jul 2019 13:25
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/24596

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