A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

Abstract

This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws [1,2] is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson-Schmidt-Turkel (JST) algorithm [3], extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge-Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.

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

“…As already shown in [1,3], appropriate geometric involutions must be satisfied by the strain measures F and H [39] as CURLF = 0; DIVH = 0.…”

“…The motion is defined through a deformation mapping x = φ(X, t) which satisfies the following mixed set of Total Lagrangian conservation laws [1,2,[32][33][34][35][36]:…”

“…In a very recent work [1], some of the authors of the present manuscript have successfully introduced a new SPH computational framework for explicit fast solid dynamics, where the conservation of linear momentum p is solved along with conservation equations for the deformation gradient F , its co-factor H and its Jacobian J. Specifically, SPH discretisation of the new mixed system of conservation laws {p, F , H, J} [3,5] is introduced in conjunction with a well-established Jameson-Schmidt-Turkel (JST) [30] stabilisation methodology.…”

“…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 [1] 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.…”

“…The main objective of the present manuscript is to further explore the SPH discretisation of the mixed based system in [1] by means of an alternative variationally consistent Streamline Upwind Petrov Galerkin (SUPG) [31] stabilisation methodology. In addition to a higher computational efficiency to that of the JST-SPH algorithm (e.g.…”