A comprehensive study on the parameters setting in smoothed particle hydrodynamics (SPH) method applied to hydrodynamics problems

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian particle method which has advantages in handling solids with extremely large deformation. Like any other numerical methods, cares must be taken to ensure its desirable accuracy and stability through considering several correction techniques in calculation. The selection of values for parameters in those correction approaches is a key step in SPH simulation, which is always difficult for new beginners to deal well with effectively. This paper examines the common inconsistency and instability problems in SPH method and studies its computational efficiency when applied to hydrodynamics problems with material strength like soil column collapse. We analyzed in detail how the correction techniques mitigate these inconsistency and instability problems. Also, the numerical testing results associate with different values for the parameters used in the correction techniques are provided for better understanding the influence of these parameters and for finding out the desirable values. It is found that (1) the SPH method is easily subjected to an inconsistency problem in the boundary area due to the boundary deficiency, and it can be treated well by adopting “virtual particles” contributing to the particle summations. (2) The numerical oscillation in SPH simulation can be mitigated effectively by artificial viscosity with the suggested parameter values. (3) The tension cracking treatment, artificial viscosity and artificial stress work well in removing the tensile instability problem in SPH method. In addition, the nearest neighboring particle searching (NNPS) algorithm, spacing ratio, smoothing length and time step influence the efficiency and accuracy of SPH method significantly. It is shown that SPH method with suggested parameters values can produce a very good result compared with the experimental result.     

基于GIS空间数据的滑坡SPH粒子模型研究

针对光滑粒子流体动力学方法（SPH）在滑坡模拟中建立粒子模型的难题,提出了基于地理信息系统（GIS）栅格数据的粒子排列与插入方法。根据该方法,建立了滑坡SPH粒子模型及相关粒子生成程序,进一步以结合摩尔-库仑破坏准则的SPH宾汉流体模型为核心,实现了运用SPH方法模拟滑坡破坏后三维运动的过程。该SPH模型在对唐家山滑坡的模拟中得到了验证,并预测了金坪子滑坡破坏后的影响范围。结果表明：基于GIS空间数据的滑坡SPH粒子模型具有可行性与良好的适用性。以GIS数据库为基础,开展滑坡灾害的模拟研究,将大大提高对滑坡等地质灾害的仿真分析,为滑坡灾害的预测与防治提供参考。     

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.     

SPH-DEM coupling method based on GPU and its application to the landslide tsunami. Part I: method and validation

Landslide-induced tsunami is a complex fluid–solid coupling process that plays a crucial role in the study of a disaster chain. To simulate the coupling behaviors between the fluid and solid, a graphics processing unit-based coupled smoothed particle hydrodynamics (SPH)-discrete element method (DEM) code is developed. A series of numerical tests, which are based on the laboratory test by Koshizuka et al. (Particle method for calculating splashing of incompressible viscous fluid, 1995) and Kleefsman et al. (J Comput Phys 206:363–393, 2005), are carried out to study the influence of the parameters, and to verify the accuracy of the developed SPH code. To ensure accurate results of the SPH simulation, the values for the diffusion term, particle resolution (1/25 characteristic length), and smoothing length (1.2 times of particle interval) are suggested. The ratio of the SPH particle size and the DEM particle’s diameter influences the accuracy of the coupling simulation between solid particles and water. For the coupling simulation of a single particle or a loose particle assembly (not contact each other) with fluid, this ratio should be smaller than 1/20; for a dense particle assembly, a ratio of smaller than 1/6 will be good.

     

A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation

The smoothed particle hydrodynamics (SPH) method was recently extended to simulate granular materials by the authors and demonstrated to be a powerful continuum numerical method to deal with the post-flow behaviour of granular materials. However, most existing SPH simulations of granular flows suffer from significant stress oscillation during the post-failure process, despite the use of an artificial viscosity to damp out stress fluctuation. In this paper, a new SPH approach combining viscous damping with stress/strain regularisation is proposed for simulations of granular flows. It is shown that the proposed SPH algorithm can improve the overall accuracy of the SPH performance by accurately predicting the smooth stress distribution during the post-failure process. It can also effectively remove the stress oscillation issue in the standard SPH model without having to use the standard SPH artificial viscosity that requires unphysical parameters. The predictions by the proposed SPH approach show very good agreement with experimental and numerical results reported in the literature. This suggests that the proposed method could be considered as a promising continuum alternative for simulations of granular flows.     

Parallel simulations of pore-scale flow through porous media

Smoothed particle hydrodynamics (SPH) is a versatile technique which can be applied to single and multiphase flow through porous media. The versatility of SPH is offset by its computational expense which limits the practicability of SPH for large problems involving low Reynolds number flow. A parallel pore-scale numerical model based on SPH is described for modeling flow phenomena in porous media. Aspects of SPH which complicate parallelization are emphasized. The speed of the method is demonstrated to be proportional to the number of processors for test cases where load balance was achieved. The parallel algorithm permits the application of SPH to more complicated porous media problems than previously considered. For such problems, best performance is achieved when several soil grains are simulated by each processor. Finally, future applications of the method and possible extensions are discussed.     

SPH法在大坝表孔泄流数值模拟中的应用

主要对光滑粒子流体动力学(SPH)法进行研究,建立了大坝表孔泄流的光滑粒子模型。将SPH数学模型应用于拉西瓦水电站表孔泄流中,提出了采用补水边界的方法来满足库区恒定水位条件,模拟了表孔泄流的流场变化及粒子运动过程。通过与物理模型实测的压力值比较,堰表面压力变化基本一致。对模拟结果进行分析,表明光滑粒子流体动力学可用于高速水流的计算模拟研究。     

基于三维并行SPH模型的土体流滑特性研究

土体的大变形流滑导致了许多地质灾害的发生,对人们的生命财产安全构成了极大的威胁,因此越来越多的研究开始关注土体的大变形流滑特性。其中,光滑粒子流体动力学（SPH）方法是常用的模拟方法之一,但SPH方法的粒子特性导致其计算时间过长,影响了在工程地质领域的进一步应用。对此,本研究基于SPH方法的基本原理、非牛顿流体理论和等效黏度概念,提出了适用于土体大变形流滑分析的三维SPH仿真模型。结合OpenMP并行计算原理,实现了SPH算法的并行优化。在此基础上,对土体流滑模型试验进行了二维和三维分析,得到了滑动距离、滑动冲击力和冲击力峰值等动力学参数,分析了计算维数和边界条件对流滑特性的影响机制。通过不同线程数下计算时间的对比,获得了计算效率随线程数的变化规律。结果证明了本文的OpenMP并行优化具有较高的计算效率,显著降低了三维SPH模拟的计算耗时,对工程地质数值方法的效率提升具有重要的借鉴意义。     

Meshless numerical modeling of brittle–viscous deformation: first results on boudinage and hydrofracturing using a coupling of discrete element method (DEM) and smoothed particle hydrodynamics (SPH)

We have developed a new approach for the numerical modeling of deformation processes combining brittle fracture and viscous flow. The new approach is based on the combination of two meshless particle-based methods: the discrete element method (DEM) for the brittle part of the model and smooth particle hydrodynamics (SPH) for the viscous part. Both methods are well established in their respective application domains. The two methods are coupled at the particle scale, with two different coupling mechanisms explored: one is where DEM particles act as virtual SPH particles and one where SPH particles are treated like DEM particles when interacting with other DEM particles. The suitability of the combined approach is demonstrated by applying it to two geological processes, boudinage, and hydrofracturing, which involve the coupled deformation of a brittle solid and a viscous fluid. Initial results for those applications show that the new approach has strong potential for the numerical modeling of coupled brittle–viscous deformation processes.     

LOQUAT: an open-source GPU-accelerated SPH solver for geotechnical modeling

Acta Geotechnica - Smoothed particle hydrodynamics (SPH) is a meshless method gaining popularity recently in geotechnical modeling. It is suitable to solve problems involving large deformation,...     

Frictional contact algorithms in SPH for the simulation of soil–structure interaction

Simulation of frictional contact between soils and rigid or deformable structure in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two algorithms are implemented into the SPH code to describe contact behavior, where the contact forces are calculated using the law of conservation of momentum based on ideal plastic collision or using the criteria of partial penetrating. In both algorithms, the problem of boundary deficiency inherited from SPH is properly handled so that the particles located at contact boundary can have precise acceleration, which is critical for contact detection. And the movement and rotation of the rigid structure are taken into account so that it is easy to simulate the process of pile driving or movement of a retaining wall in geotechnical engineering analysis. Furthermore, the capability of modeling deformability of a structure during frictional contact simulations broadens the fields of SPH application. In contrast to previous work dealing with contact in SPH, which usually use particle‐to‐particle contact or ignoring sliding between particles and solid structure, the method proposed here is more efficient and accurate, and it is suitable to simulate interaction between soft materials and rigid or deformable structures, which are very common in geotechnical engineering. A number of numerical tests are carried out to verify the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions or results from finite element method analysis. Good agreement obtained from these comparisons suggests that the proposed algorithms are robust and can be applied to extend the capability of SPH in solving geotechnical problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model

Simulation of large deformation and post‐failure of geomaterial in the framework of smoothed particle hydrodynamics (SPH) are presented in this study. The Drucker–Prager model with associated and non‐associated plastic flow rules is implemented into the SPH code to describe elastic–plastic soil behavior. In contrast to previous work on SPH for solids, where the hydrostatic pressure is often estimated from density by an equation of state, this study proposes to calculate the hydrostatic pressure of soil directly from constitutive models. Results obtained in this paper show that the original SPH method, which has been successfully applied to a vast range of problems, is unable to directly solve elastic–plastic flows of soil because of the so‐called SPH tensile instability. This numerical instability may result in unrealistic fracture and particles clustering in SPH simulation. For non‐cohesive soil, the instability is not serious and can be completely removed by using a tension cracking treatment from soil constitutive model and thereby give realistic soil behavior. However, the serious tensile instability that is found in SPH application for cohesive soil requires a special treatment to overcome this problem. In this paper, an artificial stress method is applied to remove the SPH numerical instability in cohesive soil. A number of numerical tests are carried out to check the capability of SPH in the current application. Numerical results are then compared with experimental and finite element method solutions. The good agreement obtained from these comparisons suggests that SPH can be extended to general geotechnical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow analysis of liquefied soils based on smoothed particle hydrodynamics

To overcome the disadvantages of traditional flow analysis methods for liquefied soils that exhibit fluidization and large deformation characteristics, Smoothed particle hydrodynamics (SPH) is adopted in this study to analyze the flow processes of liquefied soils. Bingham model with the use of the Mohr–Coulomb yield criterion, the concepts of equivalent Newtonian viscosity, and the Verlet neighbor list method are introduced into the framework of SPH to build an algorithm for the analysis of flowing liquefied soils. This modeling involves a simulation of physical model test of flowing liquefied soils that can be compared with numerical results. In addition, a shaking table test is selected from the literature for SPH analysis to verify the validation of the SPH method and extend its applications. The SPH simulation can reproduce the flow processes of liquefied soils and constrain estimates of the horizontal displacement, vertical displacement, and velocity of soils after liquefaction. According to the dynamic behaviors of the materials involved, designs can be implemented to improve the seismic safety of structures.     

An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure

The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of flow processes in liquefied soils using a soil–water-coupled smoothed particle hydrodynamics method

Liquefaction can result in the damage or collapse of structures during an earthquake and can therefore be a great threat to life and property. Many site investigations of liquefaction disasters are needed to study the large-scale deformation and flow mechanisms of liquefied soils that can be used for performance assessments and infrastructure improvement. To overcome the disadvantages of traditional flow analysis methods for liquefied soils, a soil–water-coupled smoothed particle hydrodynamics (SPH) modeling method was developed to analyze flow in liquefied soils. In the proposed SPH method, water and soil were simulated as different layers, while permeability, porosity, and interaction forces could be combined to model water-saturated porous media. A simple shear test was simulated using the SPH method with an elastic model to verify its application to solid phase materials. Subsequently, the applicability of the proposed SPH modeling method to the simulation of interaction forces between water and soil was verified by a falling-head permeability test. The coupled SPH method produced good simulations for both the simple shear and falling-head permeability tests. Using a fit-for-purpose experimental apparatus, a physical flow model test of liquefied sand has been designed and conducted. To complement the physical test, a numerical simulation has been undertaken based on the soil–water-coupled SPH method. The numerical results correspond well with the physical model test results in observed configurations and velocity vectors. An embankment failure in northern Sweden was selected so that the application of the soil–water-coupled SPH method could be extended to an actual example of liquefaction. The coupled SPH method simulated the embankment failure with the site investigation well. They have also estimated horizontal displacements and velocities, which can be used to greatly improve the seismic safety of structures.     

Numerical analysis on seepage failures of dike due to water level-up and rainfall using a water–soil-coupled smoothed particle hydrodynamics model

For seepage failures of dike due to water level-up and rainfall, surface infiltration and strength change induced by suction reduction are important factors; thus, numerical analysis should consider the coupling of water and soil, as well as the effect of saturation to obtain more precise failure mechanism. Based on the advanced smoothed particle hydrodynamics (SPH) method, this work proposed a two-phase-coupled SPH model in coordination with a novel constitutive model for unsaturated soils. Then, a triaxial compression test is simulated to check the applicability of the SPH method on the soil phase. After that, the failure test of a dike due to water level-up is discretized and simulated, from which the seepage process, the distribution of maximum shear strain, the slip surface, and pore water pressure are obtained. The two-phase-coupled SPH model is also applied to a slope failure test of heavy rainfall, and the results are compared to the model test. Finally, a dike failure test due to rainfall is analyzed using the proposed SPH model to reproduce the surface infiltration and suction reduction. The proposed SPH model provides several insights of seepage failures and can be a helpful tool for the analysis of dike failures induced by water level-up and rainfall.     

Modelling the flow of self‐compacting concrete

A Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

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

This 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.     

A SPH framework for dynamic interaction between soil and rigid body system with hybrid contact method

A smoothed particle hydrodynamics (SPH) framework for three-dimensional dynamic soil-multibody interaction modeling is presented, where both soils and rigid bodies are discretized using SPH particles. In the framework, soils are modeled using the Drucker-Prager model, while rigid bodies are considered with a multibody dynamics solver. A hybrid contact method suitable for three-dimensional simulations is developed to model the soil-body and body-body frictionless and frictional contacts, where contact forces are calculated based on ideal plastic collision and the unit normal/tangential vectors of the actual surface. Owing to its simplicity in contact detection and accuracy in contact force calculation, the hybrid contact method can be easily incorporated into SPH. Furthermore, graphics processing unit (GPU) parallelization is utilized to improve efficiency. The presented numerical framework and the hybrid contact method are validated using several examples. Numerical results are compared with analytical solutions and results from the literature. Furthermore, two three-dimensional simulations involving dynamic soil-multibody interaction are included to demonstrate the application.     

基于光滑质点流体动力学的海冰热力-动力数值模式

考虑海冰热力因素对其厚度、密集度的影响,在光滑质点流体动力学(SPH)基础上发展了一个海冰热力-动力数值模式。该模式既解决了传统欧拉有限差分法和质点网格法存在的数值扩散问题,同时弥补了光滑质点动力学海冰动力模式未考虑热力因素的不足,具有精确模拟冰缘线运动、计算精度高等优点。首先介绍了光滑质点流体动力学的基本原理,并对海冰生消的热力因素进行了分析,将影响冰厚和密集度的热力因素引入到光滑质点流体动力学的海冰动力模式中,得到该热力-动力模式的控制方程。应用该数值模式对渤海海冰进行了48 h数值模拟,得到了海冰厚度和速度矢量的分布规律;对JZ20-2海域的海冰厚度、冰内温度场分布以及热力因素的变化特性进行了讨论。数值模拟结果表明,该数值模式能够很好地适用于渤海海冰数值模拟,是一种有效的海冰数值模拟方法。