On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations

SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine the feasibility of using PRONTO/SPH for the analysis of various types of underwater explosion problems involving fluid-structure and shock-structure interactions. Of particular interest are effects of bubble formation and collapse and the permanent deformation of thin walled structures due to these loadings. These are exceptionally difficult problems to model. Past attempts with various types of codes have not been satisfactory. Coupling SPH into the finite element code PRONTO represents a new approach to the problem. Results show that the method is well-suited for transmission of loads from underwater explosions to nearby structures, but the calculation of late time effects due to acceleration of gravity and bubble buoyancy will require additional development, and possibly coupling with implicit or incompressible methods

A numerical and analytical investigation of Rayleigh-Taylor instability in a solid tungsten plate

The Rayleigh-Taylor instability response of an elastic-plastic tungsten plate is investigated by numerical experiments and an approximate modal analysis. The so-called ''minimum amplitude'' instability criteria derived from plasticity analyses is shown to be incomplete as a general indicator of instability or stability at very large driving pressures. Model equations are derived which are able to reproduce the basic qualitative features of the observed instability response given by the numerical calculations. 11 refs., 29 figs

Coupled explosive/structure computational techniques at Sandia National Laboratories

Simulation of the effects of explosives on structures is a challenge because the explosive response can best be simulated using Eulerian computational techniques and structural behavior is best modeled using Lagrangian methods. Due to the different methodology of the two computational techniques and code architecture requirements, they are usually implemented in different computer programs. Explosive and structure modeling in two different codes make it difficult or next to impossible to do coupled explosive/structure interaction simulations. Sandia National Laboratories has developed two techniques for solving this problem. The first is called Smoothed Particle Hydrodynamics (SPH), a relatively new gridless method comparable to Eulerian, that is especially suited for treating liquids and gases such as those produced by an explosive. The SPH capability has been fully implemented into the transient dynamics finite element (Lagrangian) codes PRONTO-2D and -3D. A PRONTO-3D/SPH simulation of the effect of a blast on a protective-wall barrier is presented in this paper. The second technique employed at Sandia uses a new code called Zapotec that combines the 3-D Eulerian code CTH and the Lagrangian code PRONTO-3D with minimal changes to either code. CTH and PRONTO-3D are currently executing on the Sandia Terraflops machine (9000 Pentium Pro processors). Eulerian simulations with 100 million cells have been completed on the current configuration of the machine (4500 Pentium Pro processors). The CTH and PRONTO-3D combination will soon be executing in a coupled fashion on this machine

Generalized Farey trees, transfer Operators and phase transitions

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spectral analysis of generalized transfer operators. Application of the thermodynamic formalism to the family reveals first and second order phase transitions and unusual properties like positivity of the interaction function.Comment: 39 pages, 10 figure

Parallel algorithm for transient solid dynamics simulations using finite elements and smoothed particle hydrodynamics

An efficient, scalable, parallel algorithm for treating contacts in solid mechanics has been applied to interactions between particles in smooth particle hydrodynamics (SPH). The algorithm uses three different decompositions within a single timestep: (1) a static FE-decomposition of mesh elements; (2) a dynamic SPH-decomposition of SPH particles; (3) and a dynamic contact-decomposition of contact nodes and SPH particles. The overhead cost of such a scheme is the cost of moving mesh and particle data between the decompositions. This cost turns out to be small in practice, leading to a highly load-balanced decomposition in which to perform each of the three major computational states within a timestep

A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure

SPH and Eulerian underwater bubble collapse simulations

SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. Previously, the SPH algorithm has been subjected to detailed testing and analysis to determine the feasibility of using the coupled finite-element/SPH code PRONTO/SPH for the analysis of various types of underwater explosion problems involving fluid-structure and shock-structure interactions. Here, SPH and Eulerian simulations are used to study the details of underwater bubble collapse, particularly the formation of re-entrant jets during collapse, and the loads generated on nearby structures by the jet and the complete collapse of the bubble. Jet formation is shown to be due simply to the asymmetry caused by nearby structures which disrupt the symmetry of the collapse. However, the load generated by the jet is a minor precursor to the major loads which occur at the time of complete collapse of the bubble

Smoothed particle hydrodynamics stability analysis

SPH (smoothed particle hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events. Recent tests of the standard SPH method using the cubic B-spline kernel indicated the possibility of an instability in the tensile regime, even though no such difficulties were observed in compression. A von Neumann stability analysis of the SPH algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function. The analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression. The instability is shown to result from an effective stress with a negative modulus (imaginary sound speed) being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm. That is, changes in the effective stress act to amplify, rather than reduce, perturbations in the strain. The analysis and the stability criterion provide insight into possible methods for removing the instability