Smoothed Particle Hydrodynamics Formulation Research Articles

Mesh-free SPH modeling of sediment scouring and flushing

A two-phase mesh-free Lagrangian model, based on the Smoothed Particle Hydrodynamics (SPH) method, is developed and evaluated for the continuum-based study of sediment-water system (a dense submerged granular flow system). The case studies are (a) sediment scouring downstream of a wall-jet, and (b) reservoir sediment flushing, both of great interest of engineers and researchers. The mesh-free Lagrangian nature of the SPH method makes the model capable of dealing with the large interfacial deformations involved in these complex water-sediment flow systems. Water and sediment materials are both treated as continuum and the governing equation of their motion are solved on a Lagrangian frame using SPH formulation. A pressure-dependent viscoplastic rheological model is used to describe the behavior of the sediment phase. A combination of Mohr–Coulomb and Shields yielding criteria (in place of commonly used Mohr–Coulomb yield criteria) is employed to determine the critical stress above which the sediment material behaves as a viscous fluid. Effect of this combination on the model results is investigated. To validate the developed numerical model, this study also provides some original experimental measurements for the test cases of this study. The results show the good compatibility of the numerical and experimental water and bed profiles. The sediment feature such as scouring and deposition areas (for wall-jet scouring case) and the sediment failure slope (for the flushing test case) are reproduced by the developed SPH model, with a good degree of accuracy. The numerical results as well as experimental measurements of this study not only provide an insight into better understanding of the complicated mechanism of sediment transport induced by rapid flow discharge, but also provide a reliable numerical tool and benchmark for simulation of such problems.

The giant impact simulations with density independent smoothed particle hydrodynamics

At present, the giant impact (GI) is the most widely accepted model for the origin of the Moon. Most of the numerical simulations of GI have been carried out with the smoothed particle hydrodynamics (SPH) method. Recently, however, it has been pointed out that standard formulation of SPH (SSPH) has difficulties in the treatment of a contact discontinuity such as a core–mantle boundary and a free surface such as a planetary surface. This difficulty comes from the assumption of differentiability of density in SSPH. We have developed an alternative formulation of SPH, density independent SPH (DISPH), which is based on differentiability of pressure instead of density to solve the problem of a contact discontinuity. In this paper, we report the results of the GI simulations with DISPH and compare them with those obtained with SSPH. We found that the disk properties, such as mass and angular momentum produced by DISPH is different from that of SSPH. In general, the disks formed by DISPH are more compact: while formation of a smaller mass moon for low-oblique impacts is expected with DISPH, inhibition of ejection would promote formation of a larger mass moon for high-oblique impacts. Since only the improvement of core–mantle boundary significantly affects the properties of circumplanetary disks generated by GI and DISPH has not been significantly improved from SSPH for a free surface, we should be very careful when some conclusions are drawn from the numerical simulations for GI. And it is necessary to develop the numerical hydrodynamical scheme for GI that can properly treat the free surface as well as the contact discontinuity.

Smoothed particle hydrodynamics: Applications to migration of radionuclides in confined aqueous systems

A smoothed particle hydrodynamics (SPH) model is presented for simulating the decay chain transport of radionuclides in confined aqueous solutions. The SPH formulation is based on the open-source parallel code DualSPHysics extended to solve the advective-diffusion equation for the evolution of the concentration field coupled to the fluid-dynamic equations, including the effects of radioactive decay of the tracer contaminants. The performance of the method is demonstrated for environmental engineering problems dealing with the transport of contaminants in still and flowing water. The results from a series of benchmark test calculations are described in two- and three-space dimensions, where the advection, diffusion, and radioactive decay modes are tested separately and in combined form. The accuracy of the present SPH transport model is shown by direct comparison with the analytical solutions and results from other SPH approaches. For a given problem, convergence of the SPH solution is seen to increase with decreasing particle size and spacing.

A smoothed particle hydrodynamics (SPH) model for simulating surface erosion by impacts of foreign particles

This paper presents a smoothed particle hydrodynamics modeling procedure to simulate surface erosion by impacts. The present SPH is improved based on the standard SPH formulation, by developing SPH formulations for the constitutive relations to describe plastic behavior and ductile fracture process. The improved SPH method is first applied to simulate impacts of particles on ductile targets. Two modified schemes in terms of density correction and kernel gradient correction are adopted to improve the accuracy of the SPH approximation. The present SPH model is applied to simulate the erosion process by angular particles. The results are compared with available experimental data, and good agreements have been achieved in terms of the crater profile and particle kinematic results.

Stable axisymmetric SPH formulation with no axis singularity

SummaryThe axisymmetric formulation of the governing equations for geomechanics in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two forms of SPH discretization for the motion equations, which are labeled as form I and form II, are proposed, and the methods to compute the hoop stress and strain terms including hoop strain rate and the acceleration introduced by the hoop stress are compared. To avoid possible singularity problem near the axis of symmetry, a perfectly smooth contact along with ghost particles are applied to prevent the real particles from overly approaching the axis of symmetry to remove this potential singularity. In addition, the Mohr–Coulomb constitutive model is implemented into the SPH formulation in describing soil behavior. Four numerical tests are carried out to validate and compare the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions and results from FEM analysis. The performance in these comparisons suggests that SPH II with hoop terms computed through direct hoop method is more stable than the others, and the adoption of contact for the symmetric axis is efficient in eliminating the singularity problem. Copyright © 2015 John Wiley & Sons, Ltd.

SPH Methods in the Modelling of Compact Objects

We review the current status of compact object simulations that are based on the smooth particle hydrodynamics (SPH) method. The first main part of this review is dedicated to SPH as a numerical method. We begin by discussing relevant kernel approximation techniques and discuss the performance of different kernel functions. Subsequently, we review a number of different SPH formulations of Newtonian, special- and general relativistic ideal fluid dynamics. We particularly point out recent developments that increase the accuracy of SPH with respect to commonly used techniques. The second main part of the review is dedicated to the application of SPH in compact object simulations. We discuss encounters between two white dwarfs, between two neutron stars and between a neutron star and a stellar-mass black hole. For each type of system, the main focus is on the more common, gravitational wave-driven binary mergers, but we also discuss dynamical collisions as they occur in dense stellar systems such as cores of globular clusters.

Suspension modeling using smoothed particle hydrodynamics: Accuracy of the viscosity formulation and the suspended body dynamics

In this paper an approach for the numerical modeling of particulate suspensions is illustrated, its implementation described and its application investigated. The numerical fluid model is based on the smoothed particle hydrodynamics (SPH) method. The suspended solids are modeled as clusters of SPH particles using a rigid body motion solver. Two different SPH formulations for the viscous stress are applied and their characteristics are compared. The influence of numerical and physical parameters on the viscosity of the system is analyzed. The rotational motion of suspended solids under shear as well as the dependency of the viscosity on the solid volume fraction is investigated and compared to analytical models. Guidelines for SPH suspension simulations are derived aiming at the minimization of numerical errors.

The eagle simulations of galaxy formation: the importance of the hydrodynamics scheme

We present results from a subset of simulations from the "Evolution and Assembly of GaLaxies and their Environments" (EAGLE) suite in which the formulation of the hydrodynamics scheme is varied. We compare simulations that use the same subgrid models without re-calibration of the parameters but employing the standard GADGET flavour of smoothed particle hydrodynamics (SPH) instead of the more recent state-of-the-art ANARCHY formulation of SPH that was used in the fiducial EAGLE runs. We find that the properties of most galaxies, including their masses and sizes, are not significantly affected by the details of the hydrodynamics solver. However, the star formation rates of the most massive objects are affected by the lack of phase mixing due to spurious surface tension in the simulation using standard SPH. This affects the efficiency with which AGN activity can quench star formation in these galaxies and it also leads to differences in the intragroup medium that affect the X-ray emission from these objects. The differences that can be attributed to the hydrodynamics solver are, however, likely to be less important at lower resolution. We also find that the use of a time step limiter is important for achieving the feedback efficiency required to match observations of the low-mass end of the galaxy stellar mass function.

Smoothed particle hydrodynamics formulation for penetrating impacts on ballistic gelatine

A particle method is applied to the investigation of impact biomechanics in the case of penetrating ballistic. A three dimensional model is proposed using the Smoothed Particle Hydrodynamics (SPH) method combined with Finite Elements (FE) method. The problem consists in the violent impact of a steel sphere on soft tissues, simulated by 20% ballistic gelatine (BG) material which is considered as a very interesting human tissue surrogate. Comparisons with experimental data are established to validate the proposed model. The results, in terms of penetrating curves, show very promising results. The use of particle methods appears to be an interesting way to model high speed loading, especially penetrating ballistic impact whose classical FE modelling can bring some important limitations in terms of mesh and element distortions.

Towards consistence and convergence of conservative SPH approximations

Typical conservative smoothed particle hydrodynamics (SPH) approximations of the gradient of a scalar field introduce two errors: one (smoothing error) is due to smoothing of the gradient by an integration associated with a kernel function; the other (integration error) is due to approximating the integration by summation over all particles within the kernel support. When particles are not on a uniform grid, the integration error leads to violation of zero-order consistency, i.e. the inability to reproduce a constant field. In this paper we confirm that partition of unity is the condition under which the conservative SPH approximation achieves both consistence and convergence. We show that this condition can be achieved by relaxing a particle distribution under a constant pressure field and invariant particle volume. The resulting particle distribution is very similar to that is typical for liquid molecules. We further show that with two different typical kernel functions the SPH approximation, upon satisfying the partition of unity property, is able to achieve very high-order of the integration error, which previously could be shown only with particles on a uniform grid. The background pressure used in a weakly compressible SPH simulation implies a self-relaxation mechanism, which explains that convergence with respect to increasing particle numbers could be obtained in SPH simulations, although not predicted by previous numerical analysis. Furthermore, by relating the integration error to the background pressure, we explain why the previously proposed transport-velocity formulation of SPH (S. Adami et al. (2013) [1]) is able to achieve unprecedented accuracy and stability.

Numerical modeling of the low-velocity impact of composite plates using a shell-based SPH method

This paper investigates the numerical modeling of low velocity impact of composite multilayered plates using the smoothed particle hydrodynamics (SPH) method. Recently the authors developed a shell-based SPH (SSPH) model for the modeling of large deformations of composite multilayered structures, has been extended to the impact modeling. The proposed new shell-based SPH formulation is based on the Mindlin–Reissner theory which accounts for transverse shearing stresses. In the present investigation, the impact modeling solution is estimated using the explicit dynamics integration scheme, together with the Hertzian contact theory, for the fast estimation of contact forces. The predictive capability of the present SSPH model is demonstrated by comparison of the results with reference solutions for the impact response of composite multilayered plates.

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.

A Smoothed Particle Hydrodynamics model for 3D solid body transport in free surface flows

This study has developed a 3D Smoothed Particle Hydrodynamics (SPH) numerical scheme to reproduce the transport of rigid bodies in free surface flows (e.g. floods, surface waves). It is based on the Euler–Newton equations for body dynamics, implemented through the SPH formalism. This scheme has been coupled to a Weakly Compressible (WC)-SPH model for the main flow, based on the semi-analytic approach (Di Monaco et al. 2011). The SPH boundary treatment of Adami et al. (2012) has been implemented and adapted to free-slip conditions to model the “fluid–solid body” coupling terms. On the other hand, the “solid–solid” (“body–body” and “body–frontier”) interactions are represented by the “boundary force particles” of Monaghan (2005). This technique has been implemented by introducing some modifications to represent the impingements of entire bodies (not only isolated particles), even at low velocities.The new model has been validated on a sequence of 2D and 3D test cases. They involve preliminary tests both with single and multiple bodies and frontiers, four water entries of falling solid wedges, and the propagation of a 3D dam break front. This is driven by the regular lift of a mobile gate, transports a floating body (6 degrees of freedom) and impacts two fixed obstacles and several solid frontiers. This last phenomenon has also been experimentally realized during this study. Validation refers to comparisons vs. measurements, Unsteady Reynolds-Averaged Navier–Stokes (URANS) results, other SPH models, analytical and theoretical solutions.

Efficient smoothed particle hydrodynamics method for the analysis of planar structures undergoing geometric nonlinearities

In the present investigation, a new modified smoothed particle hydrodynamics (SPH) method particularly adapted for the analysis of planar structures undergoing geometric nonlinearities is introduced and discussed. The problem of inconsistency which is often encountered in the classical SPH method is alleviated by introducing modifications of the kernel function and its derivatives using an explicit polynomial feature representation based on the Taylor series expansion. Tensile instabilities arising in the Eulerian-based SPH formulation which appear due to large deformations are attenuated by the introduction of a total Lagrangian formulation which is robust for large displacements/rotations. The resulting nonlinear problem is solved using the explicit dynamics time integration scheme. The validity of the proposed approach is demonstrated through two numerical applications involving geometrical nonlinearities, where the obtained results are compared to those obtained using the standard finite element method.

Shaped charge simulation using SPH in cylindrical coordinates

Purpose – The purpose of this paper is to investigate the applicability of the smoothed particle hydrodynamics (SPH) method in the jet formation process of a cylindrical-shaped charge (CSC). Different SPH formulations, suggested in other works, to other applications, are brought together in order to build a model that represents the phenomenon of detonation of a CSC in a more realistic way. Design/methodology/approach – A two-dimensional (2D) SPH formulation using cylindrical coordinates is adopted to simulate CSCs. The problem of fluid-solid interaction between the detonation wave of the explosive and the metal liner, numerically unstable due to the great difference in density between the phases, is resolved adopting the multi-phase strategy. A new proposition of artificial viscosity is incorporated in order to account the convergence effect of the liner particles toward the axis of symmetry of the charge. Two numerical examples are used to validate the formulation. In the first, the velocity and length differences between the jets formed from a CSC and a linear-shaped charge (LSC) using planar detonation on both are compared. In the second example, the effect of the conical cavity angle in the maximum jet velocity is evaluated, comparing the simulated results of CSC with four different cavity angles, with the experimental results. Findings – The results show that the 2D SPH method in cylindrical coordinates is able to simulate the detonation process of a CSC. Accordingly with the formulations used, the following conclusions can be made: the multi-phase strategy is able to capture the multi-material interface of the fluid-solid interaction between the detonation wave and the metal liner; and in the cylindrical geometry, a second artificial viscosity is necessary in order to include the convergence effect of the particles toward the axis of symmetry and obtaining more realistic results for the jet velocity. Originality/value – The applicability of the SPH method to simulate LSCs has been tested and verified in other works, but there are not references that address the application of the SPH method to simulate CSCs. CSCs are widely used in the defense industry and in the oil industries. In the oil industry, the perforating process may currently be the most common use of such a device. For this reason, it is believed that the proposed formulation in this paper is a good alternative to these specific applications.

Smoothed particle hydrodynamics in a generalized coordinate system with a finite‐deformation constitutive model

SUMMARYThis study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through‐thickness direction for a thin‐plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite‐deformation constitutive model and then verifies it by analyzing quasi‐static and dynamic problems of solids. High‐velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

DNS and LES of 3-D wall-bounded turbulence using Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics (SPH) has been used in the simulation of fluid flows for several years. Recently, SPH saw its range of applications extended to the simulation of real-world engineering applications which often concern the simulation of turbulent three-dimensional flows. However, there is a significant lack in the investigation of such turbulent flows even for simplified applications. Most three-dimensional SPH simulations that analyze properties of a turbulent flow examine the decay of isotropic turbulence, where no solid walls influence the flow. In the present paper several three-dimensional turbulent channel flows are simulated using the SPH method to address this gap in literature. The first set of simulations investigates a quasi direct numerical simulation (DNS) of a channel with reduced size. This enables evaluation of SPH as a pure Navier–Stokes solver by avoiding the introduction of turbulence models. The results show the correct reproduction of the turbulent statistics except for some fluctuations in the near wall region. The second set of simulations attempts a large eddy simulation (LES) of a standard size channel. It is shown that the present SPH formulation fails to reproduce the correct turbulent statistics and the cause for this failure is analyzed with the aide of the Taylor–Green vortex flow and attributed to incorrect reproduction of velocity–pressure interactions by the collocated and large stencil SPH discretisation.

Sedimentation in homogeneous and inhomogeneous fluids using SPH

In this paper we show how a system consisting of solid particles sedimenting in a homogeneous or a stratified liquid can be simulated with Smoothed Particle Hydrodynamics (SPH). The solid particles are assumed to be sufficiently numerous that they may be treated as a continuous fluid. In the SPH formulation there are liquid SPH particles for each type of liquid and dust SPH particles for each type of dust. The liquids are treated as slightly compressible. We focus on the key features of drag and pressure terms and we show that dust, whether buoyant or sinking in homogeneous or stratified fluids, or sedimenting in a turbulent fluid, can be simulated efficiently and accurately. The SPH formulation allows us to simulate sedimentation within irregular boundaries, or in systems containing solid bodies such as stirrers with the lower cut-off of the turbulence given by the smoothing length.

Numerical Simulation of Violent Wave Impact by ISPH Method

Smoothed particle hydrodynamics (SPH) is an attractive method for simulating unsteady flows with free-surfaces due to its Lagrangian form. Free-surface tracking or capturing is not required and hence arbitrarily complex free-surface deformations can be handled automatically. Traditionally, the simulation of incompressible fluid flow by the SPH method has been through a weakly compressible SPH formulation (WCSPH) which has low accuracy in predicting force and pressure. To overcome the limitations of the WCSPH formulation, a truly incompressible approach has been developed and proved to be more accurate and stable for many problems. In this paper a fully incompressible SPH method is applied to simulate violent interactions between free-surface and body. The calculation of forces on rigid body is improved for higher accuracy. Improved position correction technique is applied in moving boundary condition. Stability and accuracy of the present ISPH scheme are tested by dam breaking and water entry, and the results agree well with both experimental data and other numerical results.

A peridynamics–SPH coupling approach to simulate soil fragmentation induced by shock waves

In this work, a nonlocal peridynamics---smoothed particle hydrodynamics (SPH) coupling formulation has been developed and implemented to simulate soil fragmentation induced by buried explosions. A peridynamics---SPH coupling strategy has been developed to model the soil---explosive gas interaction by assigning the soil as peridynamic particles and the explosive gas as SPH particles. Artificial viscosity and ghost particle enrichment techniques are utilized in the simulation to improve computational accuracy. A Monaghan type of artificial viscosity function is incorporated into both the peridynamics and SPH formulations in order to eliminate numerical instabilities caused by the shock wave propagation. Moreover, a virtual or ghost particle method is introduced to improve the accuracy of peridynamics approximation at the boundary. Three numerical simulations have been carried out based on the proposed peridynamics---SPH theory: (1) a 2D explosive gas expansion using SPH, (2) a 2D peridynamics---SPH coupling example, and (3) an example of soil fragmentation in a 3D soil block due to shock wave expansion. The simulation results reveal that the peridynamics---SPH coupling method can successfully simulate soil fragmentation generated by the shock wave due to buried explosion.