A vertex centred Finite Volume Jameson–Schmidt–Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics

Abstract

Please cite this article in press as: M. Aguirre et al., A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics, Journal of Computational Physics (2013), http://dx.doi.org/10. 1016/j.jcp.2013.12.012 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A mixed formulation based upon the use of the linear momentum, the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two-dimensional and three-dimensional computations, respectively. The scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the Jameson-Schmidt-Turkel (JST) artificial dissipation term. The discretisation in time is performed by using a Total Variational Diminishing (TVD) two-stage Runge-Kutta time integrator. The JST algorithm is adapted in order to ensure the preservation of linear and angular momenta. The framework results in a low order computationally efficient solver for solid dynamics, which proves to be very competitive in nearly incompressible scenarios and bending dominated applications.

A Stabilised Total Lagrangian Corrected Smooth Particle Hydrodynamics Technique in Large Strain Explicit Fast Solid Dynamics

“…Neglecting dissipative effects, the dynamics of motion Φ can be described by a p-F mixed formulation system of first order conservation laws as [1,2]:…”

“…However, the above semi-discrete formulation still suffers from the appearance of accumulated numerical instabilities over a long term response. To overcome this, in contrast to the dissipative mechanism introduced by Monaghan [9] through viscous fluxes, here a nodally conservative JST stabilisation D(p a ) will be incorporated into (11), mirroring CFD techniques [2]:…”

“…The new mixed-formulation consists in a system of first order conservation laws, formally akin to Computational Fluid Dynamics (CFD) models, with linear momentum and deformation gradient being the unknown conservation variables. In [2], the technique was applied in the framework of Finite Volume method, incorporating a Jameson-Schmidt-Turkel (JST) stabilising contribution [8]. Adding JST has the dual aim of (a) accurately representing potential discontinuities in the solution, and (b) introducing artificial dissipation to it where continuous.…”

“…The adoption of a system of first order conservation laws allows CFD techniques to be introduced within the context of particle methods for solid mechanics, in the form of an adapted nodally conservative JST stabilisation [2]. Incorporation of JST stabilisation will be useful to provide artificial (numerical) dissipation and shock-capturing capabilities.…”

“…An explicit Total Lagrangian mixed momentum/strains formulation [1][2][3][4][5], in the form of a system of first order conservation laws, has been recently proposed to overcome the shortcomings posed by the traditional second order displacement-based formulation, namely: (1) bending and volumetric locking difficulties; (2) hydrostatic pressure fluctuations; and (3) reduced order of convergence for derived variables. Following the work of Bonet and Kulasegaram [6,7], the main objective of this paper is the adaptation of Corrected Smooth Particle Hydrodynamics (CSPH) in the context of Total Lagrangian mixed formulation.…”