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An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre, Miquel, Gil, Antonio J., Bonet, Javier ORCID: 0000-0002-0430-5181 and Lee, Chun Hean (2015) An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics. Journal of Computational Physics, 300. pp. 387-422. ISSN 0021-9991 (doi:10.1016/j.jcp.2015.07.029)

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Abstract

A vertex centred Jameson–Schmidt–Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 [1]) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2], [3] and [4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 [5]). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie–Grüneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

Item Type: Article
Uncontrolled Keywords: Fast dynamics; Mie–Grüneisen; Finite Volume method; Riemann solver; Incompressible; Locking; Shock capturing
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: 21 Dec 2016 15:01
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
URI: http://gala.gre.ac.uk/id/eprint/14084

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