Standard Smoothed Particle Hydrodynamics Method Research Articles

Simulation of contact interface between elastic solids using smoothed particle hydrodynamics

In recent years, the use of the smoothed particle hydrodynamics (SPH) method has increased. However, most researches have restricted the application of this method to the fluids field. Few publications have reported the use of SPH to study solid problems. Moreover, only a small amount of investigations have considered the interface when two solids are in contact. The standard SPH method is able to determine the interaction of two objects through mutual search of particles at the interface. Taking this into account, herein we report a new strategy named interfacial SPH for simulating the contact of elastic objects. In our simulations, the search domain only contained the particles of the object, and the interaction between the two objects was achieved by means of the interface force. First, the collision of two aluminium rectangles was simulated in order to test the usefulness of the simulation strategy at the linear interface. Later, the collision between two discs was simulated to test the strategy at the curved interface. Subsequently, the collision of two elastic rubber rings and the impact of a bullet on an elastic plate were simulated. These last two models showed how the strategy used in the present investigation can be applied for the simulation of large deformation of elastomers. Finally, this paper analysed the problems of applying the standard SPH method in the simulation of the interface contact between two solids. The XSPH method and the artificial stress method were used in our simulations to ensure simulation stability.

Dual-Support Smoothed Particle Hydrodynamics for Elastic Mechanics

In the standard smoothed particle hydrodynamics (SPH) method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Then, concepts of support and dual-support are defined to deal with the unbalanced interactions between the particles with different support domains. Several benchmark problems in one, two and three dimensions are tested to verify the accuracy of the modified SPH model and highlight its advantages over the standard SPH method through comparisons.

Numerical modelling of supercritical flow in circular conduit bends using SPH method

The capability of the smoothed-particle hydrodynamics (SPH) method to model supercritical flow in circular pipe bends is considered. The standard SPH method, which makes use of dynamic boundary particles (DBP), is supplemented with the original algorithm for the treatment of open boundaries. The method is assessed through a comparison with measured free-surface profiles in a pipe bend, and already proposed regression curves for estimation of the flow-type in a pipe bend. The sensitivity of the model to different parameters is also evaluated. It is shown that an adequate choice of the artificial viscosity coefficient and the initial particle spacing can lead to correct presentation of the flow-type in a bend. Due to easiness of its implementation, the SPH method can be efficiently used in the design of circular conduits with supercritical flow in a bend, such as tunnel spillways, and bottom outlets of dams, or storm sewers.

Topology optimization of plane structures using smoothed particle hydrodynamics method

SummaryThis paper presents an alternative topology optimization method based on an efficient meshless smoothed particle hydrodynamics (SPH) algorithm. To currently calculate the objective compliance, the deficiencies in standard SPH method are eliminated by introducing corrective smoothed particle method and total Lagrangian formulation. The compliance is established relative to a designed density variable at each SPH particle which is updated by optimality criteria method. Topology optimization is realized by minimizing the compliance using a modified solid isotropic material with penalization approach. Some numerical examples of plane elastic structure are carried out and the results demonstrate the suitability and effectiveness of the proposed SPH method in the topology optimization problem. Copyright © 2016 John Wiley & Sons, Ltd.

Geometrically nonlinear analysis of two-dimensional structures using an improved smoothed particle hydrodynamics method

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

Solving microscopic flow problems using Stokes equations in SPH

Starting from the Smoothed Particle Hydrodynamics method (SPH), we propose an alternative way to solve flow problems at a very low Reynolds number. The method is based on an explicit drop out of the inertial terms in the normal SPH equations, and solves the coupled system to find the velocities of the particles using the conjugate gradient method. The method will be called NSPH which refers to the non-inertial character of the equations. Whereas the time-step in standard SPH formulations for low Reynolds numbers is linearly restricted by the inverse of the viscosity and quadratically by the particle resolution, the stability of the NSPH solution benefits from a higher viscosity and is independent of the particle resolution. Since this method allows for a much higher time-step, it solves creeping flow problems with a high resolution and a long timescale up to three orders of magnitude faster than SPH. In this paper, we compare the accuracy and capabilities of the new NSPH method to canonical SPH solutions considering a number of standard problems in fluid dynamics. In addition, we show that NSPH is capable of modeling more complex physical phenomena such as the motion of a red blood cell in plasma.

Numerical simulation of the flow in a Pelton turbine using the meshless method smoothed particle hydrodynamics: A new simple solid boundary treatment

Meshless methods are getting more and more popular in order to numerically simulate physical phenomena where an interface appears and plays an important role. Thanks to its fully Lagrangian formalism, the smoothed particle hydrodynamics method (SPH) is hence well suited to simulate free surface flows. The Pelton turbine is an hydraulic turbomachinery whose flow is challenging to simulate because of the complex rotating geometry, the free surface and the interaction between the runner and the casing. The work presented here aims at adapting SPH to simulate such a flow. The standard SPH model has first been successfully used to prove the capacity of the method in order to simulate flows in Pelton turbines. As the prediction of the pressure field on the bucket's surface is a key issue, a new simple model for the treatment of solid boundary conditions is proposed. Simulations of industrial test cases, including a complete rotating runner, are finally shown.

Shear Flows in Smoothed Particle Hydrodynamics

Evolutionary calculations of rotating gaseous flows around astrophysical objects with standard smoothed particle hydrodynamics (SPH) result in inaccurate evolutions of shear flows. The large density errors (Δρ ρ) emerge within one dynamical time of the system when we adopt the mean separation of the particles as a smoothing length, h. We show that these errors originate in the definition of density and the inaccurate solution of the continuity equation in standard SPH. Standard SPH ensures the global mass conservation but does not ensure the local mass conservation. Thus, we reformulate the SPH method and find the expression of the consistent velocity field in terms of particle velocities that ensure local mass conservation. We update the particle positions using particle velocities instead of fluid velocities. These two velocities should be different theoretically. The numerical examples of the improved method are shown. The implementation of SPH described in this paper is crucial for the long-term calculations of the shear flows in differentially rotating stars, circumstellar disks, and galactic gaseous disks.

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.