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A two-step taylor-galerkin formulation for fast dynamics

A two-step taylor-galerkin formulation for fast dynamics

Karim, I.A.A, Lee, C.H.B, Gil, A.J.B and Bonet, Javier ORCID: 0000-0002-0430-5181 (2014) A two-step taylor-galerkin formulation for fast dynamics. Engineering Computations, 31 (3). pp. 366-387. ISSN 0264-4401 (Print), 1758-7077 (Online) (doi:https://doi.org/10.1108/EC-12-2012-0319)

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Abstract

Purpose - The purpose of this paper is to present a new stabilised low-order finite element methodology for large strain fast dynamics. Design/methodology/approach - The numerical technique describing the motion is formulated upon the mixed set of first-order hyperbolic conservation laws already presented by Lee et al. (2013) where the main variables are the linear momentum, the deformation gradient tensor and the total energy. The mixed formulation is discretised using the standard explicit two-step Taylor-Galerkin (2TG) approach, which has been successfully employed in computational fluid dynamics (CFD). Unfortunately, the results display non-physical spurious (or hourglassing) modes, leading to the breakdown of the numerical scheme. For this reason, the 2TG methodology is further improved by means of two ingredients, namely a curl-free projection of the deformation gradient tensor and the inclusion of an additional stiffness stabilisation term. Findings - A series of numerical examples are carried out drawing key comparisons between the proposed formulation and some other recently published numerical techniques. Originality/value - Both velocities (or displacements) and stresses display the same rate of convergence, which proves ideal in the case of industrial applications where low-order discretisations tend to be preferred. The enhancements introduced in this paper enable the use of linear triangular (or bilinear quadrilateral) elements in two dimensional nearly incompressible dynamics applications without locking difficulties. In addition, an artificial viscosity term has been added into the formulation to eliminate the appearance of spurious oscillations in the vicinity of sharp spatial gradients induced by shocks. © Emerald Group Publishing Limited 0264-4401.

Item Type: Article
Additional Information: cited By 4
Uncontrolled Keywords: Conservation laws; Fast dynamics; Finite element method; Low order; Riemann solver; Taylor-galerkin
Subjects: Q Science > QA Mathematics > QA76 Computer software
T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 03 Oct 2016 14:55
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/14093

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