Conventional Smoothed Particle Hydrodynamics Research Articles

Segment-based wall treatment model for heat transfer rate in smoothed particle hydrodynamics

We propose a new smoothed particle hydrodynamics (SPH) model that applies a segment-based wall boundary treatment method (SBWM) for heat transfer applications. We begin by focusing on natural convection simulations, where accurately modeling heat-transferring wall boundaries is crucial as they are the energy source driving the flow. A conventional SPH approach that handles such tasks is the boundary particle (BP) method, which constructs wall boundaries by placing multiple layers of particles on and behind the walls. Despite its capability of imposing accurate boundary conditions, the BP approach becomes a non-trivial task when the fluid domain involves complex boundaries. Moreover, computational costs may significantly increase because of the increased number of SPH particles necessary for modeling walls. Therefore, we utilize the recent development of SBWM to efficiently model energy-transferring wall boundaries. Specifically, SBWM is applied to the energy conservation equation for the wall heat transfer model, using the boundary truncation terms derived in this work. The SBWM-SPH method is verified in various numerical examples, comparing the results with BP-SPH and finite volume method as well as experimental data in the literature. Our study finally extends to investigating a heat exchanger with an optimized shape, demonstrating how SBWM-SPH effectively handles practical issues associated with the BP method while providing accurate heat transfer calculations for the wall.

Improvement in the Accuracy and Efficiency of Smoothed Particle Hydrodynamics: Point Generation and Adaptive Particle Refinement/Coarsening Algorithms

Improvement in the Accuracy and Efficiency of Smoothed Particle Hydrodynamics: Point Generation and Adaptive Particle Refinement/Coarsening Algorithms

Extension of finite particle method simulating thermal-viscoelastic flow and fluid–rigid body interactional process in weakly compressible smoothed particle hydrodynamics scheme

In computational non-Newtonian fluid dynamics, heat transfer has obvious effects on motions of viscoelastic fluids, mechanical mechanism of elasticity, and flow regimes. This study suggests an extended numerical scheme of smoothed particle hydrodynamics and finite particle method within density smoothing (SPH_DSFPM), which involves the discretization of smoothed particle hydrodynamics (SPH) and finite particle method (FPM) within density smoothing (DS) in the weakly compressible flow scheme. A corrected particle shifting technique is incorporated to eliminate tensile instability and inhomogeneity near solid boundaries. A corrected dynamic solid coupled boundary is introduced to deal with casting molding within high-pressure operations, which has a good compatibility between virtual particle method and repulsive force model. Numerical results show that the present scheme has the nearly lower relative error (0.5%) than conventional SPH (2.6%) in the case of evolutionary thermal-viscoelastic Poiseuille flow and heat effects have active influences on velocity, pressure variations for viscoelastic fluid flow around periodic circular cylinders. Three different printing modes of moving printers significantly generate into differentiated forming regimes through high-pressure extrusion. Adaptive particle distributions possess robust flow evolutions, by which the shocked jets can be tracked well and the sinking velocities of wedge entering into solutions can be numerically probed well considering different cuspidal biting angles. In the case of macroscopic fluid–rigid body interactions, the statistical degree of deviation on probed forces with experiments is relatively 4.35% and that is 12.5% for SPH. The proposed numerical scheme has a good performance on improved accuracy, convergence, and stability for simulating transient thermal-viscoelastic flows.

A general smoothed particle hydrodynamics (SPH) formulation for coupled liquid flow and solid deformation in porous media

The method of smoothed particle hydrodynamics (SPH) has been recently developed to study the coupled flow-deformation problems in porous material and considerable success has been achieved comparing to traditional mesh-based method, especially for treating large deformation and post-failure. However, computational challenges remain for the hydro-mechanical boundary treatment as well as the accuracy and stability of the numerical scheme. It is shown that the use of conventional SPH operator for the solution of the coupled problem can lead to several issues including numerical instabilities, inaccuracies and unphysical particle clumping as well as particle disorders near the boundary. To address these issues, a general SPH scheme with enhanced accuracy for saturated/unsaturated porous material is proposed in this paper. An improved SPH formulation for seepage analysis is proposed to allow an accurate prediction of liquid flow in porous material. A new stabilisation technique that combines the use of a density diffusion term, a modified particle shifting algorithm, and a new viscous damping term is developed to further improve the accuracy, stability and robustness of the proposed method. The implementations of stress boundary conditions and hydraulic boundary conditions in SPH, such as confining stress, hydraulic head, infiltration/evaporation, and potential seepage face, using either wall boundary particles or free-surface domain particles, are discussed in detail. A range of benchmark examples is adopted to verify the validity of the present coupled framework. The proposed model is finally applied to simulate the failure process of embankment dam due to rapid drawdown. Results indicate that the methodology proposed herein can be a promising tool for the analysis of the coupled hydro-mechanical process in porous material involving large deformations.

Regularized SPH model for soil–structure interaction with generalized frictional boundary

AbstractThis paper proposes a regularized smoothed particle hydrodynamics (SPH) scheme to solve the problems of tensile instability and stress noise in large‐deformation soil–structure interaction. Particle shifting and stress regularization are combined to maintain uniform stresses and particle distributions. A generalized frictional boundary condition is presented to model soil–structure interfaces with abitrary friction coefficients. A modified particle shifting technique is developed to regularize particles near the frictional boundaries. Furthermore, GPU acceleration algorithm is adopted to improve the efficiency. The proposed scheme is compared with the conventional SPH methods using numerical examples, including the collapse of three‐dimensional granular column, the collapse of the cohesive soil, and pipe penetrates into soft clay. The comparison indicates that the proposed regularized SPH model can give highly accurate results for large‐deformation soil–structure interaction problems with arbitrary friction coefficient.

SPH modeling of substance transport in flows with large deformation

The velocity field in coastal and oceanic currents is mostly non-uniform, which will result in irregular particle distribution when the fluid is represented by an amount of moving discrete particles as in smoothed particle hydrodynamics (SPH). When the non-uniformity of the flow is big, i.e., with large deformation, the conventional SPH method can hardly solve the associated advection-diffusion process (e.g., substance transport). To accurately simulate the substance transport in flows with large deformation, two types of particle shifting techniques (PSTs) are incorporated into the conventional SPH in this paper. One is based on current particle distance, and the other is based on Fick’s law. In the second type, the repulsive force (RF) term for suppressing the paring instability that occurs in particle shifting technique (PST) is studied and the effect of the kernel function is examined. By introducing a particle disorder measurement, the simulated results of SPH with the two types of PSTs and their modifications are evaluated and the influence of the shifting magnitude is analyzed. The suggestions for how to set reasonable parameters in PSTs are provided by a systematic parametric study. For further illustration, the simulation of the anisotropic diffusion is also examined. To give reliable reference solutions, the high-resolution modified total variation diminishing Lax Friedrichs scheme with Superbee limiter (MTVDLF-Superbee) with fine mesh is also implemented. The validated Lagrangian particle model with optimized PST is applied to a practical application.

Numerical Simulation Low Filling Ratio of Sway Sloshing in the Prismatic Tank Using Smoothed Particle Hydrodynamics

Sloshing is one of challenging problem in the free surface flow, because is dealing with large deformation of fluid. The present paper was carried out of numerical sloshing in the prismatic tank that resemble of LNG membrane type carrier. Pressure sensor was used to validate the dynamic pressure in low filling ratio of tank. Forced oscillation motion in sway with f = 1.08 Hz and amplitude of motion 6.52 mm. A single, and double vertical baffles are used to reduce dynamic pressure and hydrodynamic force. The ratio of baffle heigh with water depth is 0.9. A meshless computational fluid dynamics (CFD) was used to reproduce sloshing in the prismatic tank. Smoothed particle hydrodynamics (SPH) is one of the major meshless CFD. In addition, The advanced visualization was performed using Blender version 2.92. The results showed the vertical baffles effectively reduce the dynamic pressure and hydrodynamic force. Moreover, the advanced visualisation made sloshing simulation more realistic, and attracting compare conventional SPH post-processing.

Application of normalized SPH method to inviscid fluid flows with large deformation of free surface

A new normalized smoothed particle hydrodynamics (SPH) method has been presented recently and applied to transient solid mechanics problems of small deformation. The method can overcome boundary deficiency of the conventional SPH method without troublesome inversion of corrective matrix and provide convenience for treating boundary conditions. In this paper, a formulation of the normalized SPH method is derived for modeling inviscid fluid flows with large deformation of free surface. The treatment of dynamic free surface boundary conditions in the present method is addressed and theoretically compared with that in the conventional SPH method. A method based on kernel estimation is proposed for calculation of boundary summation and compared with the method based on α-shape. The normalized SPH method is applied to modeling inviscid free surface flows. Numerical results demonstrate that the present method is capable of modeling large deformation of free surface and can produce higher accuracy than the conventional SPH method, especially at boundary regions. The newly developed kernel estimation method for the calculation of boundary summation is more efficient than the α-shape-based method, and makes the computational efficiency of the normalized SPH method close to the conventional SPH method. To simulate violent free surface flows, a particle shifting technique is introduced in the present method. With this technique, the method is applied to simulating extremely large deformation, fragmentation and reconnection of free surface.

Large deformation analysis of geomaterials using stabilized total Lagrangian smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) based on Eulerian kernels is widely-used in large deformation analysis of geomaterials. Despite being popular, it has tensile instability and rank-deficiency; thus, it needs several numerical treatments to be stable. In this work, a stabilized total Lagrangian SPH method is presented, which is inherently free of tensile instability. A stiffness-based hourglass control algorithm is employed to cure the instability caused by rank-deficiency. Periodic update of reference configuration is employed to allow the modeling of large deformation. Numerical examples are presented to show the performance of the method. The comparison between the presented method and the conventional smoothed particle hydrodynamics are discussed. The influences of hourglass control and configuration update are also investigated. It is found that the presented method is robust and can model large deformation and plastic flows in geomaterials. Particularly, the stabilized method delivers better stress results.

A shock-capturing scheme with a novel limiter for compressible flows solved by smoothed particle hydrodynamics

There are many compressible flows involving strong discontinuities in nature and engineering applications. Their behaviors are complicated by the existence of shock waves, rarefaction waves and contact discontinuities. To investigate these flows, a shock-capturing scheme based on smoothed particle hydrodynamics (SPH) is proposed. In this scheme, Roe’s approximate Riemann solver cooperated with a novel limiter is embedded into the SPH governing equations to capture shocks. This limiter is simple and effective to control numerical dissipations, and the use of this limiter eliminates the tunable artificial viscosity as required by the conventional SPH. Additionally, to restore the accuracy limited by heterogeneous particle distribution that is usually encountered in the simulation of strongly-compressible flows, the gradient operator in the continuity equation is corrected by a renormalization procedure. Last but not least, for initial particle distribution, unlike the equal mass particle distribution commonly used in compressible SPH simulations, the equal spacing particle distribution is adopted in this scheme, which makes it much easier to model multidimensional problems. The present scheme has been verified by a set of benchmark tests involving contact discontinuities, extreme shock waves and strong rarefaction waves, some of which are firstly simulated by the SPH method.

Development of time-space adaptive smoothed particle hydrodynamics method with Runge-Kutta Chebyshev scheme

Smoothed particle hydrodynamics (SPH) method is a Lagrangian particle method that has been widely used for solving complex mechanics problems. To reduce the SPH computational cost, the adaptive SPH (ASPH) with time-varying particle distribution has been proposed using the particle splitting and merging techniques. However, the particle splitting in the adaptive SPH results in a decreased time step due to the reduced particle spacing and thus requires an increased amount of computing time. In the present work, an explicit Runge-Kutta Chebyshev time stepping scheme is implemented within the adaptive SPH, by including the stabilizing substeps into the Runge-Kutta integration method with the use of the Chebyshev polynomials. The number of stabilizing substeps in a single SPH time step can be adaptive after particle splitting while the Runge-Kutta integration time step remains the same. Therefore, the proposed SPH algorithm is adaptive in both time and space domains. Representative example problems are simulated using the developed time-space adaptive SPH method. It is demonstrated that, as compared to the standard SPH and the conventional adaptive SPH with varying particle distribution only, the presented time-space ASPH method exhibits much higher efficiency without compromising accuracy and the superiority in terms of stability.

Efficient thermomechanical analysis of functionally graded structures using the symmetric SPH method

Tailoring the thermal and mechanical properties plays an important role in manufacturing and designing functionally graded material (FGM) which is often applied in high temperature gradient environment. The present investigation will address the basics of thermoelastic problem solved by means of a specific meshless smoothed particle hydrodynamics (SPH) method. The inconsistency of the conventional SPH method was improved by introducing the symmetric SPH (SSPH) technique, where function derivatives can be approximated by the function values in the support domain. Hence, the heat conduction and balance equations become a series of algebraic equations, which can be solved efficiently. The result accuracy achieved by the proposed approach was demonstrated in solving several numerical examples in comparison to available results in the literature. The effect of the gradation indexes on the thermoelastic behavior was also considered.

Meshless analysis of bi-directional functionally graded beam structures based on physical neutral surface

More and more attention has been paid on the two-directional functionally graded materials (FGMs) applied in harsh heat environment. A novel meshless model is established for the bending analysis, based on the Smoothed Particle Hydrodynamics (SPH) method. To improve the prediction accuracy, the conventional SPH method is improved by the symmetric SPH method starting from the Taylor series expansion. Moreover, the neutral surface position of the bi-directional FG beam is determined and the third order Reddy-Bickford beam theory based on this exact neutral surface is adopted. The governing equations are deduced for FGB composed by two or four different materials and then discretized by the proposed method. The present model is verified by comparison of the deflection with the solution obtained in literature and a self-programmed finite element code. The deformation of the beam with different gradient indexes and boundary conditions is also investigated.

Modeling hydrate-bearing sediment with a mixed smoothed particle hydrodynamics

Marine gas hydrate is an important energy source while its extraction may induce environmental problems such as subsea landslide, which is usually challengeable for numerical simulation due to the marine environment with high pressure and the existence of gas hydrate. Smoothed particle hydrodynamics (SPH) is a Lagrangian particle method which is attractive in modeling problems with large deformations and fluid–solid interactions (FSI) for continuum and granular materials. However, the conventional SPH suffers from numerical instability when modeling the soil mechanics with the high confining stress. A mixed SPH is developed in this study to simulate hydrate-bearing sediment with the characteristics of high confining stress. In the mixed SPH model, the conventional SPH is used to discretize the momentum equations, and the kernel gradient correction (KGC) SPH is used to discretize strain and spin rate tensors. In order to consider the effect of hydrate saturation on the strength of soil-hydrate material, an existing linear model is applied into the mixed SPH to define the mechanic parameters of soil-hydrate material. The mixed SPH method is validated by several examples and the obtained numerical results are in close agreement with experimental observations. Finally, the mixed SPH method is used to model landslide of hydrate bearing sediments. The results show that the saturation of hydrate has important impact on the stability of hydrate bearing sediments.

A Study on Stable Regularized Moving Least-Squares Interpolation and Coupled with SPH Method

The smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics. Generally, a high-precision interpolation is required to calculate the particle physical attributes and their derivatives for the boundary treatment and postproceeding in the SPH simulation. However, as a result of the truncation of kernel function support domain and irregular particle distribution, the interpolation using conventional SPH interpolation experiences low accuracy for the particles near the boundary and free surface. To overcome this drawback, stable regularized moving least-squares (SRMLS) method was introduced for interpolation in SPH. The surface fitting studies were performed with a variety of polyline bases, spatial resolutions, particle distributions, kernel functions, and support domain sizes. Numerical solutions were compared with the results using moving least-squares (MLS) and three SPH methods, including CSPH, K2SPH, and KGFSPH, and it was found that SRMLS not only has nonsingular moment matrix, but also obtains high-accuracy result. Finally, the capability of the algorithm coupled with SRMLS and SPH was illustrated and assessed through several numerical tests.

Numerical study via total Lagrangian smoothed particle hydrodynamics on chip formation in micro cutting

Numerical simulation is an effective approach in studying cutting mechanism. The widely used methods for cutting simulation include finite element analysis and molecular dynamics. However, there exist some intrinsic shortcomings when using a mesh-based formulation, and the capable scale of molecular dynamics is extremely small. In contrast, smoothed particle hydrodynamics (SPH) is a candidate to combine the advantages of them. It is a particle method which is suitable for simulating the large deformation process, and is formulated based on continuum mechanics so that large scale problems can be handled in principle. As a result, SPH has also become a main way for the cutting simulation. Since some issues arise while using conventional SPH to handle solid materials, the total Lagrangian smoothed particle hydrodynamics (TLSPH) is developed. But instabilities would still occur during the cutting, which is a critical issue to resolve. This paper studies the effects of TLSPH settings and cutting model parameters on the numerical instability, as well as the chip formation process. Plastic deformation, stress field and cutting forces are analyzed as well. It shows that the hourglass coefficient, critical pairwise deformation and time step are three important parameters to control the stability of the simulation, and a strategy on how to adjust them is provided.

Simulation of mixed‐mode fracture using SPH particles with an embedded fracture process zone

SummaryThis paper focuses on the modelling of mixed‐mode fracture using the conventional smoothed particle hydrodynamics (SPH) method and a mixed‐mode cohesive fracture law embedded in the particles. The combination of conventional SPH and a mixed‐mode cohesive model allows capturing fracture and separation under various loading conditions efficiently. The key advantage of this framework is its capability to represent complex fracture geometries by a set of cracked SPH particles, each of which can possess its own mixed‐mode cohesive fracture with arbitrary orientations. Therefore, this can naturally capture complex fracture patterns without any predefined fracture topologies. Because a characteristic length scale related to the size of the fracture process zone is incorporated in the constitutive formulation, the proposed approach is independent from the spatial discretisation of the computational domain (or mesh independent). Furthermore, the anisotropic fracture responses of materials can be naturally captured thanks to the orientation of the fracture process zone embedded at the particle level. The performance of the proposed approach demonstrates its potentials in modelling mixed‐mode fracture of rocks and similar quasi‐brittle materials.

Research on the Effect of Particle Distribution on the Crack Propagation in Shaped Energy Blasting Based on the Smoothed Particle Hydrodynamics

Conventional smoothed particle hydrodynamics (SPH) methods suffer from disadvantages, such as difficult initial particle configuration, uneven distribution of generated particles, and low computational efficiency when applied to numerical simulation of shaped charge blasting. In this research, to overcome these problems, a modified SPH method that generates the particle configuration through self-adaptive optimization is developed by the combined application of MATLAB and LS-DYNA. The results presented in this paper demonstrate that the modified configuration method solves the problem of uneven distribution of particles in complex geometry domains by providing a more uniform smoothed particle distribution than the conventional SPH method. Furthermore, the results from the application of these two methods to the bidirectional-shaped charge blasting problem reveal that the defects in the particle configuration in the conventional SPH method lead to the development of main cracks in both the shaped and the unshaped directions. However, with the self-adaptive optimization method, the main cracks develop only in the shaped direction. In addition, the equivalent stress difference between the shaped and unshaped directions, 0.7 ms after detonation, is 120 MPa with the modified method. This is 85 MPa more than that with the conventional method.

Angular Particle Impact on Metallic Surfaces with Dynamic Refinement SPH

Because of the mesh-less nature of the smoothed particle hydrodynamics (SPH) method, it has been widely used to simulate surface erosion by impact(s) of angular particles. However, previous SPH models usually adopted uniform resolution for the whole computing domain, which is not conductive to achieve a balance between computational efficiency and prediction accuracy. In this study, numerical models for simulating angular particle impact on metallic surfaces are established by using the SPH method. The innovation of this study is that a dynamic refinement procedure is implemented in the conventional SPH model. The critical step of the procedure is to split individual SPH particles according to the plastic strain and the contact force, such that the particle resolution near the impact site is locally refined. The optimal separation parameter and the smoothing distance of the new particles are determined such that the error produced by the refinement in the kernel summation is small. The present model is validated and verified by simulating single and multiple particle impact on OFHC copper targets. Results show that the dynamic refinement procedure increases the prediction accuracy of the erosive crater and saves the computing effort.

A smoothed particle element method (SPEM) for modeling fluid–structure interaction problems with large fluid deformations

Fluid–structure interaction (FSI) problems with large fluid deformations can be a great challenge for numerical simulations using conventional methods. In this paper, we propose a novel hybrid approach of an improved Smoothed Particle hydrodynamics and smoothed finite Element Method (SPEM) for modeling FSI problems. In SPEM, the edge-based smoothed finite element method (S-FEM) is developed in Lagrangian frame and is used for the first time to model both elastic structures and incompressible flows. For fluid regions with large deformations, the associated finite elements are adaptively converted into particles and the corresponding regions are subsequently modeled using the decoupled finite particle method (DFPM), which is an improved smoothed particle hydrodynamics (SPH) method suitable for modeling incompressible flows with free surfaces. A ghost particle-based interface algorithm to couple existing S-FEM elements and DFPM particles is developed in SPEM to implement the modeling of FSI problems. As the smoothed FEM and decoupled FPM are enhanced FEM and SPH respectively and DFPM is only used for local fluid regions with large deformations, it is expected that SPEM is more accurate and more efficient than the existing coupling approaches of conventional FEM and SPH. Five numerical examples are tested using the proposed SPEM and the comparative studies with results from other sources reveal that SPEM is an effective approach for modeling FSI problems with large fluid deformations.