An upwind vertex centred finite volume solver for Lagrangian solid dynamics

Aguirre, M., Gil, A. J., Bonet, J. and Lee, C. H. (2015) An upwind vertex centred finite volume solver for Lagrangian solid dynamics. Journal of Computational Physics, 300, pp. 387-422. (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], [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:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Lee, Dr Chun Hean
Authors: Aguirre, M., Gil, A. J., Bonet, J., and Lee, C. H.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Computational Physics
Journal Abbr.:JCP
Publisher:Elsevier
ISSN:0021-9991
ISSN (Online):1090-2716
Published Online:21 July 2015

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