A variationally consistent Streamline Upwind Petrov-Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics

This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for explicit fast solid dynamics. The proposed methodology explores the use of the Streamline Upwind Petrov-Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson-Schmidt-Turkel (JST) stabilisation recently presented by the authors in Lee et al. (2016) in the context of a conservation law formulation of fast solid dynamics. The work introduced in this paper puts forward three advantageous features over the recent JST-SPH framework. First, the variationally consistent nature of the SUPG stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations. This differs from the JST-SPH framework, where an a posteriori projection procedure was required to ensure global angular momentum preservation. Second, evaluation of expensive harmonic and bi-harmonic operators, necessary for the JST stabilisation, is circumvented in the new SUPG-SPH framework. Third, the SUPG-SPH framework is more accurate (for the same number of degrees of freedom) than its JST-SPH counterpart and its accuracy is comparable to that of the robust (but computationally more demanding) Petrov-Galerkin Finite Element Method (PG-FEM) technique explored by the authors in Lee et al. (2014), Gil et al. (2014,2016), Bonet et al. (2015), as shown in the numerical examples included. A series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm. The resulting SUPG-SPH framework is therefore accurate, robust and computationally efficient, three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations.