Application of an improved contact algorithm for penetration analysis in SPH

Shock waves in accretion flows onto compact objects are very important to transform the gravitational potential energy into radiation. The possibility that they exist also around black holes has been suggested years ago by Hawley, Smarr and Wilson (1984a, 1984b). Recently it has been shown that there is a wide range of parameters (essentially angular momentum and specific energy [for adiabatic flows] or temperature [for isothermal flows]) for which steady shock configurations are possible (Chakrabarti 1990, Chakrabarti & Molteni, 1993). Recent analytical calculations have shown the stability for isothermal and adiabatic shocks (Lu 1997; Nakayama, 1994). This fact has great astrophysical relevance since, in this way, the emission due to the shock is not a transient episode but can be a permanent mechanism responsible for the radiated energy. Here we review the relevant results obtained in the last few years through numerical simulations by a novel technique named Smoothed Particles Hydrodynamics (SPH). We concentrate on the axisymmetric problems which are done using cylindrical coordinates. The plan of this contribution is the following: in Section 2 we describe the SPH numerical method in cylindrical coordinates for axisymmetric problems, then, in Section 3 and its subsections, we give the basic ingredients, analytical equations, of the physical problem of accretion flows onto Black Holes. In Section 4 we present some results of the simulations and comment on them.

There is few research about contact problem for a rigid surface with an arbitrary shape in SPH. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty It is proposed a new method that can determine the parameters for a penetration and a penetration rate used in the penalty method. The reproducing condition is adopted to correct the deficiency of kernel on the boundary. In order to calculate a penetration of particles, after checking boundary particles for deformable body, boundary normal vectors were determined on the rigid surface. Numerical simulations for models which have rigid surface with an arbitrary shape were conducted to validate the proposed method in 2D Cartesian and cylindrical coordinate. The results of those analysis represent that the contate algorithm proposed in this study works properly.

Finite element-smoothed particle hydrodynamics adaptive method in simulating debris cloud

Shot peening is a complex surface-treating process which is usually employed to improve the fatigue strength of metallic part or members. In dealing with shot peening simulation, existing literatures apply finite element method (FEM) to establish only a single shot or several shots models, thus the effect of a mass of shots impacting repeatedly and the interaction among adjacent shots are ignored. To overcome these defects of FEM models, smoothed particle hydrodynamics (SPH) coupled FEM modeling is presented, in which the shots are modeled by SPH particles and the target material is modeled by finite elements. Contact algorithm is used to simulate the interaction between shots and target. Utilizing this model, material model for shots is established, the relationships between compressive residual stress and peening frequencies, coverage, and velocities are analyzed. Steady compressive residual stress can be gotten by multiple peening; higher coverage can improve the compressive residual stress; faster velocities can induce greater and deeper maximum residual stress in target subsurface. The simulation results agree well with the existing experimental data. The study will not only provide a new powerful tool for the simulation of shot peening process, but also be benefit to optimize the operating parameters.

In this paper, the spatially dispersive finite-difference time-domain (FDTD) method in cylindrical coordinates is applied to model the hyperlenses formed by a tapered array of metallic wires. The hyperlens device is modeled using the effective medium theory as a frequency and spatially dispersive dielectric. The gradual increase in spacing between wires along the radial direction of the physical structure is represented by the reduction of plasma frequency of the effective medium. Simulation results show that the image transfer and magnification capability of the hyperlens is insensitive to its transverse dimension. A seven-fold magnification of a subwavelength source distribution transferred to a distance of three wavelengths is demonstrated using a hyperlens with high plasma frequency at its front interface.

This paper presents an improved smoothed particle hydrodynamics (SPH) model through a rigorous mathematical derivation based on the principle of virtual work, aiming at establishing a three-dimensional numerical wave tank overcoming excessive numerical dissipation that has been usually encountered in traditional SPH models in practical applications. In order to demonstrate the accuracy and convergence of the new scheme, the viscous damping of a standing wave is first investigated as a quantitative validation, with particular attention on emphasizing (1) its physical rationality with respect to energy conservation and (2) its ability to alleviate wave over-attenuation even using fewer neighbors compared with the traditional δ-SPH model. Subsequently, several fully three-dimensional engineering problems, with respect to water wave propagation and the interaction with structures, are investigated to demonstrate the effectiveness of the new scheme in alleviating wave over-attenuation. It is demonstrated that the present model can be performed with relatively few neighbors (i.e., higher computational efficiency) to obtain accurate and convergent numerical results for those SPH simulations involving long-term and long-distance water wave propagation.

Based on the principle of virtual works, a multiphase smoothed particle hydrodynamics (SPH) model is further developed from the foundation of Hu X Y et al. (2006) and Grenier N et al. (2009). In the present model, the surface tension force implementation suitable for the multiphase flows with a large density ratio is applied, and this allows a good continuity at the multiphase interface. Artificial displacement correction is applied to keep the particles distributing uniformly in the whole flow field, and therefore any artificial viscous term is never needed; this is very important in the numerical simulation of viscous flows since the introduction of artificial viscosity changes the Reynolds number. Background pressure and interface sharpness force are added in the equation of state and the equation of momentum respectively to ensure the multiphase interface stability and smoothness; this is essential in the simulation of multiphase flows with large density difference at the multiphase interface. Two types of viscosity expressions suitable for multiphase flows are introduced and analyzed; the conclusion is that the formula proposed by Morris et al. (1997) and its similarly derived forms can give more accurate results. In the numerical validations, an oscillating droplet test is applied first to confirm the accuracy of the surface tension model and good results are achieved. This demonstrates that the artificial displacement and the interface sharp force will make negligible effects to the surface tension implementation. After that, two classic quantitative benchmarks of rising bubbles are simulated and the results of SPH agree well with the reference data. Moreover, in the two numerical benchmarks, the effect of the artificial displacement, the choice of the viscosity expression, and the type of the kernel function are compared and finally an optimal combination of these numerical aspects is recommended. Based on the above numerical investigations, the splitting process of an initially circular bubble is simulated and the numerical results agree well with the experimental data. In the last numerical case, the process of chasing and merging between two rising bubbles in vertical direction is simulated, based on which the mechanisms of these interesting interactions between two rising bubbles are analyzed. It is demonstrated in the present work that further improved multiphase SPH model may provide a potential method for the research of bubble dynamics.

A numerical simulation method of natural fragment formation and injury to human thorax

Nonlocal elastoplasticity and/or damage models in terms of gradient or integral of strain or internal state variables have been proposed to regularize softening with localization in model-based simulation of failure evolution. For transient problems, the numerical oscillations due to semi-discretization in space make the evaluation of higher order terms a difficult task in avoiding numerical failure such as premature cracking. In this preliminary study, an integrated MPM (material point method) and SPH (smoothed particle hydrodynamics) numerical scheme is proposed to implement a nonlocal model via the gradient of plastic strain, with an application to a one-dimensional bar under impact. The MPM is used to discretize the continuum region without the need for master/slave nodes at the contact surface, while the smoothing operator and particle approximation based on the SPH are adopted on the material points to reduce the unphysical oscillations and facilitate the evaluation of strain gradient. A parametric investigation is performed to illustrate the effects of controlling parameters on the evolution of localized softening. It is demonstrated that integrating nonlocal constitutive modeling with spatial discretization might yield an effective procedure for predicting and evaluating failure evolution.

The iterative method of Schwarz domain decomposition (DDS) was used as a dynamic contact algorithm for two and more contacting 3D bodies allowing the consideration of the solution of the stress-strain state problem in the standard statement for each of the contacting body and the high-level parallelization of the solution process. According to the offered iteration algorithm, two steps are performed in each iteration, where the contact conditions for the displacement and stresses are fulfilled in turn for the nodes on the contact surface. The specific feature of the realization of the dynamic contact problem was the combination of the iteration procedures for the refinement of the contact problem solution according to the Newton-Raphson algorithm with the iterations of the DDS method. As the test calculation results have shown, the use of the Schwarz contact algorithm and the HHT-α scheme in combination with the mass redistribution method on the contact boundary is a reliable, stable and sufficiently accurate way for the numerical integration of the contact problems at impact interaction. Finally, accuracy of the proposed method is verified by a conservation of momentum through three contact examples.

Numerical simulations of water entries based on a three-dimensional parallelized Smoothed Particle Hydrodynamics (SPH) model developed by Ecole Centrale Nantes are presented. The aim of the paper is to show how such SPH simulations of complex 3D problems involving a free surface can be performed on a super computer like the IBM Blue Gene/L with 8,192 cores of Ecole polytechnique fédérale de Lausanne. The present paper thus presents the different techniques which had to be included into the SPH model to make possible such simulations. Memory handling, in particular, is a quite subtle issue because of constraints due to the use of a variable-h scheme. These improvements made possible the simulation of test cases involving hundreds of million particles computed by using thousands of cores. Speedup and efficiency of these parallel calculations are studied. The model capabilities are illustrated in the paper for two water entry problems, firstly, on a simple test case involving a sphere impacting the free surface at high velocity; and secondly, on a complex 3D geometry involving a ship hull impacting the free surface in forced motion. Sensitivity to spatial resolution is investigated as well in the case of the sphere water entry, and the flow analysis is performed by comparing both experimental and theoretical reference results.

Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations

A coupled smoothed particle hydrodynamic and finite particle method: An efficient approach for fluid-solid interaction problems involving free-surface flow and solid failure

This paper aims to provide a coupled finite element method (FEM) and smoothed particle hydrodynamics (SPH) approach capable of reproducing the blast response in rock. In the proposed approach, SPH is used to simulate large deformation and fracture of rock at the near detonation zone, while the FEM is adopted to capture the far field response of the rock. The explosive is modelled explicitly using SPH. The numerical simulations are carried out using LS-DYNA. The interaction of the SPH particles and FEM elements was modelled by the node to surface contact, and for the interactions between explosive and rock SPH parts node to node penalty based contact was used. In the present study, the Johnson and Holmquist constitutive model is used for rock. Jones–Wilkins–Lee model is used for TNT explosive. It is found that the preliminary numerical simulation reproduces some of the well-known phenomena observed experimentally by other researchers. The numerical results indicate that the coupled SPH-FEM approach used in this work can be applied to simulate effectively both compressive and tensile damage of rock subjected to blast loading.

A magnetic induction based underwater communication link is evaluated using an analytical model and a custom Finite-Difference Time-Domain (FDTD) simulation tool. The analytical model is based on the Sommerfeld integral, and a full-wave simulation tool evaluates Maxwell's equations using the FDTD method in cylindrical coordinates. The analytical model and FDTD simulation tool are then compared and used to predict the system performance for various transmitter depths and optimum frequencies of operation. To this end, the system bandwidth, signal to noise ratio, and the magnitude of the induced voltage are used to estimate the expected channel capacity. The models show that in seawater, a relatively low-power and small coil may be capable of obtaining a throughput of 40 to 300 kbps, for the case where a transmitter is at depths of 1 to 3 m and a receiver is at a height of 1 m.