Smoothed Particle Hydrodynamics Particles Research Articles

A hybrid Finite Volume-Smoothed Particle Hydrodynamics approach for shock capturing applications

A hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach for shock capturing in compressible fluids is presented. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. New FVM-SPH coupling approaches are explored, including online SPH particle injection and deletion around time persistent SPH regions around shocks. The SPH simulation is coupled to the FVM simulation through boundary particles surrounding the active SPH regions, with FVM values interpolated to SPH boundary particles at each timestep. Values in active SPH regions are similarly interpolated to the overlying FVM mesh at each timestep. The performance of the hybrid FVM-SPH scheme in comparison to the individual FVM and SPH methods on two-dimensional test problems is assessed. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy, although it remains slower than the FVM. This hybrid SPH algorithm may enable future compressible fluid simulations with more extensive capabilities than grid-based methods alone, offering potential applications in modeling fluid–structure interaction and solid deformation and fracturing in blast simulations. Further research will focus on applying the hybrid method to three-dimensional blast problems, where the relative computational cost reduction is expected to be more significant.

Halted-pendulum Relaxation: Application to White Dwarf Binary Initial Data

Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.

Study of the Interaction between Fluid Flow and Solid Particle with Smoothed Particle Hydrodynamics Method

This study shows the interaction between the solid particles with water flow occurring caused by the piping erosion phenomenon. This modelling study was executed by using Smoothed Particle Hydrodynamics (SPH) as a numerical approach with the DualSPHysics platform. The water flow is assumed as laminar flow with a low Reynolds number of 100 and 200. The solid particle is modelled as a circular-shaped particle with a fixed position. The result evaluated in this research is the coefficient of hydrodynamics force on the solid particle. In the case of interaction between one circular-shaped solid particle against the water flow, it is found that by increasing the size of volume control, the output will have higher accuracy. The accuracy of this model is also improved by elongating the maximum time simulation to ensure that the SPH particle has spread evenly throughout the volume control. In the case of interaction between two solid particles against water flow at different distances, it is found that increasing the distance between the two particles reduce the force, drag coefficient, and lift coefficient of each particle. Furthermore, the increase of distance between the two particles makes vortices form in a single dominant frequency and it affects the strouhal number.

Numerical model of the Gross–Pitaevskii equation for rotating Bose–Einstein condensates using smoothed-particle hydrodynamics

This study proposed a new numerical scheme for vortex lattice formation in a rotating Bose–Einstein condensate (BEC) using smoothed particle hydrodynamics (SPH) with an explicit real-time integration scheme. Specifically, the Gross–Pitaevskii equation was described as a complex representation to obtain a pair of time-dependent equations, which were then solved simultaneously following discretization based on SPH particle approximation. We adopt the fourth-order Runge–Kutta method for time evolution. We performed simulations of a rotating Bose gas trapped in a harmonic potential, showing results that qualitatively agreed with previously reported experiments and simulations. The geometric patterns of formed lattices were successfully reproduced for several cases, for example, the hexagonal lattice observed in the experiments of rotating BECs. Consequently, it was confirmed that the simulation began with the periodic oscillation of the condensate, which attenuated and maintained a stable rotation with slanted elliptical shapes; however, the surface was excited to be unstable and generated ripples, which grew into vortices and then penetrated inside the condensate, forming a lattice. We confirmed that each branch point of the phase of wavefunctions corresponds to each vortex. These results demonstrate our approach at a certain degree of accuracy. In conclusion, we successfully developed a new SPH scheme for the simulations of vortex lattice formation in rotating BECs.

On the accuracy of SPH formulations with boundary integral terms

Handling boundaries in smoothed particle hydrodynamics (SPH) is believed to be one of the most critical problems in studies and applications of SPH. In the last two decades, excellent progress has been made in exploring the evaluation of the boundary integral terms directly to improve SPH approximation on the boundary. However, because of the fundamental difficulties, formulations in this regard are difficult to be made consistent when using SPH particle approximations, which significantly affect the solution accuracy. In this work, an intensive investigation is made in carefully analyzing the order of accuracy of the SPH approximation when boundary integral terms are included. Both kernel consistent and particle consistent boundary integral formulations of SPH are examined in great detail. Notably, a novel particle consistent boundary integral formulation for first-order derivatives is derived. An approximation of this new formulation, which is weakly consistent, is also discussed. The theoretical analysis and numerical experiments show that the SPH with particle consistent boundary integral formulation outperforms significantly in terms of accuracy compared to the correction factors used in traditional SPH implementations.

Numerical modeling of shaped charge jet penetration into ceramic–metal double-layered medium using smoothed particle hydrodynamics

The prediction of the damage effects of shaped charge projectile to ceramic–metal multi-layered target is a challenging task to address. In this paper, the smoothed particle hydrodynamics (SPH) method is applied to simulate the penetration of the metal jet generated by the shaped charge detonation into ceramic–metal double-layered plates. The presented SPH model incorporates different equations of states. Moreover, the elastic-perfectly plastic constitutive model and the Johnson–Holmquist-II material constitutive model were employed for modeling the mechanical behaviors of the solid materials in this study. Firstly, simulation of the high velocity impact process of a ceramic ball on a ceramic–metal double-layered plate was conducted to validate the presented constitutive model. After the validation of the numerical model, simulations of penetration of a shaped charge into a double-layered ceramic–metal plate by using millions of SPH particles were conducted. The simulation results (perforation diameter and debris cloud) are in good agreement with the available experimental data, which shows that our in-house SPH solver is capable of tackling the shaped charge detonation and its penetration into multi-layered structures very well. Furthermore, the presented SPH model can reproduce different types of fracture patterns observed in experiments and their dynamic formation processes.

Modelling of thrombus formation using smoothed particle hydrodynamics method.

In this paper a novel model, based on the smoothed particle hydrodynamics (SPH) method, is proposed to simulate thrombus formation. This describes the main phases of the coagulative cascade through the balance of four biochemical species and three type of platelets. SPH particles can switch from fluid to solid phase when specific biochemical and physical conditions are satisfied. The interaction between blood and the forming blood clot is easily handled by an innovative monolithic FSI approach. Fluid-solid coupling is modelled by introducing elastic binds between solid particles, without requiring detention and management of the interface between the two media. The proposed model is able to realistically reproduce the thromboembolic process, as confirmed by the comparison of numerical results with experimental data available in the literature.

Multiscale SPH simulations of viscoelastic injection molding processes based on bead-spring chain model

In this paper we present an extension of a multiscale smoothed particle hydrodynamics (SPH) method to transient viscoelastic injection molding processes. Specifically, we use the method presented by Xu and Yu, J. Non-Newtonian Fluid Mech. 229 (2016) pp. 27–42, in which the bead-spring chain model is employed to describe the viscoelastic behavior of the fluid without resort to a closed-form constitutive equation. Moreover, to resolve the heavy computation and the time-consuming problem, an efficient parallel algorithm, including parallelizations of both SPH particles and Brownian configuration fields, is developed. To validate the algorithm, we first simulate the viscoelastic Couette flow based on Hookean dumbbell, FENE dumbbell, and FENE chain models. The SPH results are compared with the analytical solutions or those obtained by other methods. The parallel performances of the algorithm are analyzed. Then, we extend the method to the challenging injection molding problem. A number of numerical examples including the injection molding of an F-shaped cavity in two dimensions and a door handle in two and three dimensions are investigated. Some molecular information such as the molecular stretch, the orientation angle, and the mean configuration thickness are displayed. It is found that the injection molding processes could be successfully investigated by SPH from a micro perspective. The proposed parallel algorithm is essential for the efficient simulation of injection molding processes. The maximum speedup can reach more than 130 for the case of the door handle in three dimensions.

Surface Gravity Wave Generation and Interference Effects in SPH Models

DualSPHysics is an open-source implementation of the SPH (smoothed-particle hydrodynamics) particle mechanics model built for applications in coastal and ocean engineering, suitable for cases possessing complex surface boundary conditions and interactions of fluids with bound objects. This work seeks to examine the general plausibility of utilization of DualSPHysics for modeling cases involving the diffraction and interference effects of surface gravity waves. The work attempts to seek optimized parameters for wave generation intended to be used in diffraction and interference cases at lower simulation resolutions by taking advantage of simulation parameters such as gravity, construct simple examples to demonstrate the plausibility to use the model with more complex cases (possibly involving diffraction and interference off lattices), and validate wave behaviors (related to gravity) within the model using accepted theories of surface wave propagation. The paper identifies several limitations whose mitigation was deemed necessary for further success applying DualSPHysics to diffraction and interference problems, as well as further analysis and tests needed for a complete assessment of the tested cases.

A coupled SPH-DEM approach for modeling of free-surface debris flows

A Lagrangian mesh-less model is proposed to simulate fluid–solid flows with multiple-sized solids, i.e., millimeter-sized particle and larger-sized debris. Considering the difference in the size of solid phases, a hybrid resolved and unresolved model is established based on the coupling method of smoothed particle hydrodynamics (SPH) and discrete element method (DEM). SPH is used to model fluid, and the locally averaged Navier–Stokes equations are adopted as governing equations. DEM is used to model the particle–particle interactions, and the unresolved description of hydrodynamic forces including drag and buoyancy is established. The large-sized debris is modeled as the rigid body, which is discretized by particle elements having both SPH and DEM characteristics, where SPH particle elements are involved in the closure of the SPH fluids, and DEM particle elements interact with the solid particles following the contact law. The numerical model is validated and verified by several examples, including single-particle sedimentation, collapse of cylinder columns, and debris dam break. Results show that the present model reproduces general features of the complex fluid–solid flow with free surfaces. The advantage of the hybrid model is that it can deal with the fluid–solid flow problem with both small particles and large objects at a suitable resolution, and it is especially good at dealing with the free surface flow problem. A discretization for the modeling of debris flows is proposed based on the coupled SPH-DEM method. The novelty of the work is a coupled resolved–unresolved scheme for the free surface flow with multi-sized solids. The present scheme allows using a uniform resolution by bridging the size difference between small-scale solid particles and large-scale debris. The unresolved model of fluid-particle flow is efficient because the fluid resolution can be configured comparably to the particle size. The unified nature of the model allows the combination of resolved and unresolved simulations in the same computational domain.

Modelling the Lyman-α forest with Eulerian and SPH hydrodynamical methods

ABSTRACT We compare two state-of-the-art numerical codes to study the overall accuracy in modelling the intergalactic medium and reproducing Lyman-α forest observables for DESI and high-resolution data sets. The codes employ different approaches to solving both gravity and modelling the gas hydrodynamics. The first code, Nyx, solves the Poisson equation using the Particle-Mesh (PM) method and the Euler equations using a finite-volume method. The second code, CRK-HACC , uses a Tree-PM method to solve for gravity, and an improved Lagrangian smoothed particle hydrodynamics (SPH) technique, where fluid elements are modelled with particles, to treat the intergalactic gas. We compare the convergence behaviour of the codes in flux statistics as well as the degree to which the codes agree in the converged limit. We find good agreement overall with differences being less than observational uncertainties, and a particularly notable ≲1 per cent agreement in the 1D flux power spectrum. This agreement was achieved by applying a tessellation methodology for reconstructing the density in CRK-HACC instead of using an SPH kernel as is standard practice. We show that use of the SPH kernel can lead to significant and unnecessary biases in flux statistics; this is especially prominent at high redshifts, z ∼ 5, as the Lyman-α forest mostly comes from lower-density regions that are intrinsically poorly sampled by SPH particles.

Application of the Godunov-Type Corrective Smoothed Particle Method to Impulsive Load Studies

The smoothed particle hydrodynamics (SPH) method is based on the kernel particle approximation, which is sensitive to the uniformity of the SPH particle distribution in the computational domain; that is, all SPH particles must be distributed evenly in the computational domain. These factors significantly influence the practical application of the SPH method. Meanwhile, calculating the sum near the boundaries of the computational domain may cause boundary defect problems since there are insufficient particles in the support domain, thus often resulting in relatively high errors in numerical simulation results near boundaries. To address these problems, the kernel particle approximation discrete process was corrected based on the traditional SPH method, and the corrected SPH method, the Godunov-type corrective smoothed particle method (CSPM), was formulated by introducing Riemann decomposition. In this study, the traditional SPH method and Godunov-type CSPM method were applied in a comparative study of discontinuous function problems, 1D shock tubes and 1D detonation waves. According to the analysis results, the Godunov-type CSPM method can not only effectively improve the calculation accuracy and compatibility of the traditional SPH method in discontinuous shock wave problems but also increase the accuracy of the traditional SPH method in capturing strong discontinuities.

3D simulations of AGB stellar winds

Aims. We present the implementation of the treatment of particle ejection and dust nucleation in the smoothed particle hydrodynamics (SPH) code PHANTOM. These developments represent the first step toward a more complete modeling of dust-driven winds emanating from asymptotic giant branch (AGB) stars that can be used for comparison with high resolution imaging of these stars. Methods. The AGB outflow is modeled by injecting the SPH particles from a spherical inner boundary. This boundary is a series of concentric shells, with the AGB star at its center, and the particles are positioned on these shells on the vertices of an isocahedron geodesic surface. The outermost shell is ejected with a predefined radial velocity, and subsequent lower shells replenish the ejected ones, all rotated randomly to improve the isotropy of the outflow. The physical properties of the particles on these shells are set by solving the 1D analytic steady wind equations. The formation of dust is calculated starting from a compact chemical network for carbon-rich material, which creates the building blocks of the solid-state particles. Subsequently, the theory of the moments is used to obtain dust growth rates, without requiring knowledge on the grain size distribution. Results. We tested our implementation against a series of 1D reference solutions. We demonstrate that our method is able to reproduce Parker-type wind solutions. For the trans-sonic solution, small oscillations are present in the vicinity of the sonic point, but these do not impact the trans-sonic passage or terminal wind velocity. Supersonic solutions always compare nicely with 1D analytic profiles. We also tested our implementation of dust using two formalisms: an analytic prescription for the opacity devised by Bowen and the full treatment of carbon-dust formation. Both simulations reproduce the 1D analytic solution displaying the expected additional acceleration when the gas temperature falls below the condensation temperature.

Numerical modeling of wave-porous structure interaction process with an SPH model

<p indent="0mm">This paper presents a smoothed particle hydrodynamics (SPH) model for modeling the fluid-structure interaction of waves and porous structures with high permeability. In the proposed model, the solid and fluid phases are discretized with two types of SPH particles; thus, the model can be applied to study heterogeneous problems directly. We use a varying smoothing length model to preserve the numerical accuracy inside and outside the porous media. The SPH artificial numerical viscosity mode is used in this study to achieve stable numerical solutions. Furthermore, the well-known Forchheimer model has also been used to model the flow in porous media with high Reynolds numbers. With the current model, the experimental observation of the water-level evolutions of a wave-dam interaction benchmark problem has been reproduced. We have also investigated a scenario with a heterogeneous distribution of porosities and compared the simulation results to those of the benchmark problem. Consequently, our model can determine how porous structures can reduce the kinetic energy induced by the waves around the coast.

Slope stability and post-failure analysis of soil-rock-mixture using the modified 2D DDA-SPH method

Soil-rock-mixture (SRM), consisting of high-strength rock blocks and low-strength soil, is widely distributed in nature. In traditional methods such as limit equilibrium methods , this geomaterial was simplified as a uniform medium without considering the influence of rocks due to its heterogeneity and complex physical and mechanical properties. A coupling method that bridges discontinuous deformation analysis (DDA) for rock simulation and smoothed particle hydrodynamics (SPH) for soil simulation is a promising tool for SRM problems. In this study, the 2D coupled DDA-SPH method is extended to the applications of stability and post-failure analysis of SRM slopes. First, the determination of the contact spring stiffness in the contact algorithm is presented and the reasonable value is discussed. Then, to eliminate the oscillations in some simulations with polygonal rock blocks inside the soil, the contact algorithm is modified by implementing a special treatment for the contact between the SPH particles and the convex vertices of DDA blocks. In addition, the criterion based on the distribution of plastic zone is used to define the critical stable state of the slope when applying the strength reduction technique for stability analysis, and its effectiveness is demonstrated. Finally, a series of numerical analyses are carried out, and through these numerical simulations, some conclusions and suggestions can be reached. • A determination of the contact spring stiffness in the DDA-SPH coupled method was proposed and discussed. • The oscillations in the simulations with polygonal rock blocks inside soil has been eliminated by modifying the contact algorithm. • The effectiveness of the modified method has been demonstrated through several numerical simulations. • The modified method has showed advantages in modeling soil-rock-mixture materials.

Study on dynamic response of debris flow to pipeline with defect

Based on the Finite Element Method (FEM) and the Smooth Particle Hydrodynamics (SPH) coupling method, this paper established full-size multi-physical field coupling model of debris flow impacting pipeline. By simplifying mud into Bingham fluid, this paper studied the dynamic response law of pipeline with defect and intact pipeline (pipeline without defect) under the joint action of mud and block stone, established the displacement equations of the pipeline under impact, thus obtained the displacement, stress and strain characteristics of different pipeline positions at different impact moment. The results showed that numerical simulation of dispersing mud into SPH particles can well simulate the movement process of mud splashing and detour flow. The maximum displacement occurred in the middle part of the pipeline. For the intact pipeline, the main failure was caused by the instantaneous impact of the mud, however, for the pipeline with defect, the dominant failure factor changed from the mud impact to the stone impact. This study provided a new pathway and theoretical reference for disaster prevention and control of pipelines in debris flow section.

SPH-DEM modeling of the seismic response of shallow foundations resting on liquefiable sand

In this study, the seismic response of shallow foundations resting on a liquefiable soil layer is modeled using a coupled smoothed particle hydrodynamics (SPH)-discrete element method (DEM) scheme. In this framework, the soil deposit is represented by an assembly of DEM particles and the fluid domain is lumped into a set of SPH particles carrying local fluid properties. The averaged forms of Navier-Stokes equations dictate the motion of the fluid-particle mixture and the interphase forces are estimated using well-known semi-empirical equations. A saturated soil-foundation system with an average contact pressure of 50 kPa was created using the coupled scheme. The foundation block was composed of a collection of DEM particles glued together by high-stiffness bonds. No-penetration boundary condition was applied to all sides of the foundation block to allow for fluid-foundation interaction. The model was subjected to a strong base acceleration and the response was analyzed and compared to the free-field. The ground settlement in the soil-foundation system mostly originated from co-seismic deviatoric deformations while volumetric strains were the main contributing factor at the free-field. In addition, the impact of soil permeability on the seismic response of the soil-foundation system was examined by changing the pore fluid viscosity. According to the results, as the soil permeability decreased, smaller excess pore pressures developed beneath the footing thanks to the slower migration of pore fluid from the sides and bottom, and a larger magnitude of soil strength and stiffness was maintained in the expansive zone. As a result, the system with the lowest permeability experienced the smallest foundation settlement while the foundation acceleration amplitude was the highest in this case. The results also showed that the percentage of post-shaking settlement appreciably increased in the lower-permeability deposits. The results of this study were compared with the published centrifuge studies that showed good qualitative consistency. • A SPH-DEM scheme is utilized to model the seismic response of shallow foundations on liquefiable soils. • Averaged form of Navier-Stokes equations are used to describe the pore fluid motion in the mixture. • The foundation block was composed of a collection of DEM particles glued together by high-stiffness bonds. • No-penetration boundary condition was applied to all foundation sides to allow for fluid-foundation interaction. • The results of this study qualitatively agree with published centrifuge studies.

A consistent multiphase flow model with a generalized particle shifting scheme resolved via incompressible SPH

This contribution outlines a multiphase flow solution method developed in conjunction with the incompressible smoothed particle hydrodynamics (SPH) discretization. We present (a) a generalized multiphase particle shifting technique that maintains a regular particle distribution and prevents interface particle mixture; and (b) a color-function-based repulsive force for the pressure gradient term at the correction step of the projection method, which improves the interface smoothness while minimizing the contribution of artificial forces. The solution approach employs consistent discretizations for the gradient and Laplacian operators, which enhances the accuracy of the spatial differential operators. The surface tension model embraced relies on the continuum surface stress (CSS) formulation. The solution methodology proposed is broadly applicable since i) the generalized particle shifting scheme applies to both 2D and 3D simulations, and ii) the interface smoothness and the solution robustness can be preserved with density ratios up to 1:1000, and viscosity ratios up to 1:100. The solution method has been used in conjunction with a set of benchmark problems to demonstrate its accuracy by comparing simulation results against analytical solutions, results from other numerical methods, and experimental data. The method has been implemented to leverage GPU-enabled parallelism and used herein to solve complex physics phenomena encountered in 3D bubble rising and coalescence problems via simulations that include over one million SPH particles.

Improved Smoothed Particle Hydrodynamics (SPH) Model for Simulation of Abrasive Water-Jet (AWJ)

Simulation of surface erosion by impact of abrasive water-jet (AWJ) is challenging for traditional mesh-based numerical methods, because it involves complex phenomena related to fluid–solid interaction, material removal and free surface flows. In this study, the surface erosion mechanism of ductile target materials by AWJ is investigated based on the smoothed particle hydrodynamics method (SPH, a mesh-free method). The water-jet, abrasives and solid target are all discretized with a series of SPH particles. The water-jet is modeled as a continuous fluid flow, the target material is modeled as a elastic–plastic material, and the abrasives are modeled as rigid bodies. The SPH model is improved by combining several correction algorithms and techniques, which help us to increase the stability and the accuracy of the simulation. The density diffusion correction term is introduced for water-jet, which reduces the pressure noise and makes the pressure field more stable. The dynamic boundary algorithm is used for the abrasives, and the pressure distribution around the abrasive is improved. The interactions among the water-jet, abrasives and solid target are realized by different contact algorithms. The dynamic process of plastic deformation, material removal and crater generation of the target material under AWJ impact can be simulated by the improved SPH model. The proposed model could be useful in the applications of AWJ machining and metal surface erosion.

A weakly compressible smoothed particle hydrodynamics framework for melting multiphase flow

In this study, the transient process of solid–liquid phase change is modeled and simulated by the multiphase smoothed particle hydrodynamics (SPH) method. First, to simulate the interfacial behaviors of melt liquids, the multiphase SPH model is established for immiscible viscous fluids with a large density ratio, where the environmental liquid surrounding the solid phase is considered, and the surface tension of the melt liquid can be accurately modeled by the continuum surface force method. Based on the multiphase model, the thermal dynamics model is incorporated to describe the heat conduction process. The solid–liquid phase change is realized by directly switching the state of the concerned SPH particle, where the absorbed latent heat is computed by the phase change model. Second, the model is validated by several simulation cases, including the Stefan problem, hydrostatic pressure of the evolving fluid interface, rising of two bubbles, and square droplet deformation, and the effects of numerical parameters on simulation accuracy and stability are also discussed. Third, the integrated SPH model is applied to simulate molten droplet formation and dropping processes. The results show that an initial solid–liquid interface disappears during the melting process, and new liquid–liquid interfaces gradually form and evolve under the action of surface tension, gravity, and viscosity. Phenomena such as thin-layer fluid dynamics and capillary instabilities are also reproduced, showing the effectiveness of the model for handling multiphase flow with heat conduction and phase change.