Improved Smoothed Particle Hydrodynamics Method Research Articles

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields, and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids. However, traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time, and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids. In this paper, a universal multiscale method coupling an improved smoothed particle hydrodynamics (SPH) and multiscale universal interface (MUI) library is presented for viscoelastic flows. The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain. We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows. In the first example, the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions. The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain. In the second example, the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics (DPD) method. The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain. Moreover, transferring different physical quantities has an important effect on the numerical results.

Study on Water Entry of a 3D Torpedo Based on the Improved Smoothed Particle Hydrodynamics Method

The water entry of a torpedo is a complex nonlinear problem, involving transient impact, free surface deformation, droplet splashing, and fluid–structure coupling, which poses severe challenges to traditional mesh methods. The meshless smoothed particle hydrodynamics (SPH) method shows unique advantages in capturing the complex features of the water entry of the torpedo at different entry angles. However, it still suffers from some inherent shortcomings, such as low surface discretization accuracy, poor discretization flexibility, and low calculation efficiency. In this study, an improved adaptive SPH algorithm is proposed to investigate the water entry of the torpedo accurately and efficiently. This method integrates meshless point generation and adaptive techniques simultaneously. The numerical results demonstrate that when the torpedo vertically enters the water at different velocities, the induced impact loads acting on the head of the torpedo fluctuate significantly with two peak values in the initial stage and thereafter stabilize in a later stage. The impact load acting on the torpedo, the entry depth of the torpedo, the splash height of the droplets, and the size of the cavity generated around the torpedo increase with the increment in the entry velocity. When the torpedo enters the water at different entry angles under the same initial entry velocity, both the vertical and the horizontal movements of the torpedo are observed, which results in more complex variations in parameters along the x- and y-axes. The findings and the corresponding numerical method in this study can provide a certain basis for the future designs of the entry trajectory and the structural bearing capacity of torpedoes.

A modified SPH framework of for simulating progressive rock damage and water inrush disasters in tunnel constructions

To date, numerically simulating the Fluid–Solid Interaction (FSI) and the entire process of host rock damage and water inrush involved in tunnel construction relies intensively on hybrid methods of two or more numerical codes, which commonly encounter deficiency in learning, modelling and computation. A modified framework of Smoothed Particle Hydrodynamics (SPH), the Coupled Discontinuous SPH (CDSPH) method, was developed to simulate cracking, contacting and large deformation of rock blocks, free surface flow and the FSI for water/mud inrush disasters in tunnel construction through water–rich stratums. The failed SPH particles were transformed to discontinuous particles and new contacts between these particles were formed to simulate the frictional slip and separation/compression between fracture walls. The improved SPH method was employed to a water inrush case of a tunnel and the simulation results indicate that the entire process of progressive rock damage, water inrush and flooding are precisely reproduced by the improved method. The greater kinematic viscosity of fluids and rock wall thickness can increase the flow velocity and hence increasing the impact pressure of floods, and the failure pattern of the rock wall changes from partial outburst to complete failure. Vulnerability analysis of the water inrush reveals a complete damage status for people, vehicles and Non-RC frame buildings, and a moderate to complete damage to RC frame buildings at the tunnel portal. This single code is capable of simulating the behaviour of rocks, fluids and their interactions in catastrophic disasters that is potentially applicable to a wide spectrum of surface and subsurface problems involving FSI.

An active learning SPH method for generalized Newtonian free surface flows

This paper presents an active learning smoothed particle hydrodynamics (ALSPH) method to simulate generalized Newtonian free surface flows. First, an improved smoothed particle hydrodynamics (ISPH) method is established to obtain more reliable results for free surface flows by coupling the modified kernel gradient, the artificial viscosity, the density diffusive term, and the optimized particle shifting technique. Second, based on data and Gaussian process regression (GPR), an active learning strategy is developed to provide an effective constitutive relation. It is the first time that the ISPH method is combined with GPR to simulate generalized Newtonian free surface flows. Not only can the constitutive relation of any generalized Newtonian fluid in nature be accurately predicted, but a small amount of sampling data is also able to ensure accuracy over a wide range of the shear deformation rate. The challenging droplet impact and dam break are first modeled to validate the ISPH method. Due to the lack of an analytical constitutive relation for an arbitrary generalized Newtonian fluid in nature, the Cross model is then adopted and offers the required data to validate the ALSPH method. The results indicate that the learned constitutive relation is quite consistent with the analytical one and the simulation results match well. In addition, predictive accuracy and time consumption are proven. Furthermore, to verify the applicability of the learned constitutive relation, the jet buckling case and the jet entering the static fluid case are modeled. The good performance demonstrates the ALSPH method has a promising prospect of applications in simulating complex flows in nature.

Improved MPS models for simulating free surface flows

Two improved Laplacian models are introduced in this study for more accurate simulation of free surface flows in the context of the moving particle semi-implicit (MPS) method, a well-known mesh-less approach. The Euler equations are the governing equations of these flows without considering viscous forces which are solved in the Lagrangian frame by the MPS and two-step projection methods for spatial and temporal discretization, respectively. Considering the similarity between the MPS and SPH (smoothed particle hydrodynamics) methods, one of the introduced Laplacian models is formulated by a corrective matrix firstly proposed in an improved SPH method [28]. The other modified Laplacian model is also derived from the divergence of a newly developed MPS gradient model proposed for solving elasticity problems [33]. The higher accuracy of these methods compared to the classic SPH, MPS and even three modified SPH and MPS Laplacian models [7, 34, 44] is verified by solving 2D Poisson equations. Moreover, the excellent performance of the Laplacian models and the improved gradient model in obtaining smooth pressure field is validated by solving three benchmark free surface flows. Furthermore, the problem of wave damping in the original MPS computations can be resolved by using the applied models.

A Joint Johnson-Cook-TANH Constitutive Law for Modeling Saw-Tooth Chip Formation of Ti-6AL-4V Based on an Improved Smoothed Particle Hydrodynamics Method.

Titanium alloy is a crucial structural material in the modern aerospace field due to its strong corrosion resistance and strength, low density, and reduced sensitivity to vibration load and impact load, as well as its ability to resist expansion in the case of cracks. However, during high-speed cutting of titanium alloy, it is prone to periodic saw-tooth chip formation, which can cause high-frequency fluctuations in the cutting force, aggravate the vibration of the machine tool system, and ultimately reduce the tool's service life and the workpiece's surface quality. In this study, we investigated the influence of the material constitutive law in modeling the Ti-6AL-4V saw-tooth chip formation and proposed a joint material constitutive law JC-TANH which was developed based on the Johnson-Cook constitutive law and the TANH constitutive law. It has two advantages of the two models (JC law and TANH law), which means that it can describe the dynamic properties accurately, the same as the JC model, not only under low strain but also under high strain. The most important thing is that it does not need to fit the JC curve at the early stage of strain changes. Additionally, we established a developed cutting model, which integrates the new material constitutive, and the improved SPH method to predict chip morphology, cutting and thrust forces which are collected by the force sensor; we also compared the data with experimental results. Experimental results show that this developed cutting model can better explain the shear localized saw-tooth chip formation and correctly estimate its morphology as well as the cutting forces.

Using an improved SPH algorithm to simulate thermo-hydro-mechanical-damage coupling problems in rock masses

The Thermo-Hydro-Mechanical-Damage (THMD) process inside rock structures is a complex multi-field coupling problem, which is also regarded as the hotspot worldwide. In view of this situation, a fracture mark ξ is introduced to reflect the “active” or “failure” mode of Smoothed Particle Hydrodynamics (SPH) particles, which can simulate rock progressive cracking characteristics. The solid-water interaction modes and the damaged particles - water particles transformation algorithms are embedded into traditional SPH program to simulate the water-stress coupling problems. The heat conduction equations are programmed into SPH, which can reach the goal of modeling the temperature-stress coupling problems. Results show that: By coupling the parameter transformations between water and solid particles, the thermo-hydro-mechanical-damage simulation is then realized. Three numerical examples are carried out to validate the improved THMD method. Finally, an engineering numerical model of a typical tunnel is established, and the THMD coupling processes under complex conditions are simulated, which shows that the improved SPH method can simulate rock THMD multi-field coupling problems. The research results will help understanding the rock THMD coupling mechanisms, meanwhile, it can also promote the applications of SPH method into THMD modeling.

Shear Damage Simulations of Rock Masses Containing Fissure-Holes Using an Improved SPH Method

Fissures and holes widely exist in rock mechanics engineering, and, at present, their failure mechanisms under complex compress and shear stress states have not been well recognized. In our work, a fracture mark, ξ, is introduced, and the kernel function of the smoothed-particle hydrodynamics (SPH) is then re-written, thus realizing the fracture modelling of the rock media. Then, the numerical models containing the fissures and holes are established, and their progressive failure processes under the compress and shear stress states are simulated, with the results showing that: (1) the improved SPH method can reflect the dynamic crack propagation processes of the rock masses, and the numerical results are in good agreement with the previous experimental results. Meanwhile, the improved SPH method can get rid of the traditional mesh re-division problems, which can be well-applied to rock failure modeling; (2) the hole shapes, fissure angles, fissure lengths, fissure numbers, and confining pressure all have great impacts on the final failure modes and peak strengths of the model; and (3) in practical engineering, the rock masses are in the 3D stress state, therefore, developing a high performance 3D SPH program and applying it to engineering in practice will be of great significance.

An improved SPH method for simulating crack propagation and coalescence in rocks with pre-existing cracks

An improved smoothed particle hydrodynamics (SPH) method is proposed to simulate the failure process of rock samples with pre-existing cracks under compression loads. By improving the kernel function of SPH, the brittle fracture characteristics of rock materials are captured. In the improved SPH, a prefabricated node segment (PNS) method is used to generate arbitrarily complex open or closed cracks, avoiding the kernel truncation caused by digging out particles. In order to improve numerical stability, the tension instability control (TIC) technique is embedded in the momentum equation. Moreover, the improved SPH adopts the coupled dynamic buffer solid boundary treatment algorithm, which reduces the configuration of boundary virtual particles, makes the application of boundary conditions more efficient. The accuracy of the improved SPH method and the feasibility of TIC technique are verified by a benchmark example. Then, the effect of the center dislocation spacing of the pre-existing cross crack on the failure mode and compressive strength of rock samples is studied. In addition, the effects of confining pressure on the coalescence type and penetration failure mode of cracks in a rock sample with two pre-existing cracks are also investigated. The numerical results agree well with the experimental results, which verifies the accuracy and validity of the improved SPH method.

Improved smoothed particle dynamics simulation of eXtended Pom-Pom viscoelastic fluid

Viscoelastic fluids widely exist in nature and industrial production, and the study of their complex rheological properties has important academic value and application significance. In this work, an improved smoothed particle hydrodynamics (SPH) method is proposed to numerically simulate the viscoelastic flow based on the eXtended Pom-Pom (XPP) model. In order to improve the accuracy of the calculation, a kernel gradient correction discrete format without kernel derivative calculation is adopted. In order to prevent fluid particles from penetrating the solid wall, an enhanced boundary processing technology is proposed. To eliminate the tensile instability, an artificial stress is coupled into the momentum equation of conservation. Based on the XPP model, the viscoelastic Poiseuille flow and the viscoelastic droplet impacting solid wall problem are simulated by using the improved SPH method. The effectiveness and advantages of the improved SPH method are verified by comparing the SPH solutions with the solutions from the analytical method or finite difference method. The convergence of the improved SPH method is further evaluated by using several different particle sizes. On this basis, the influences of rheological parameters such as Reyonlds number <i>Re</i>, Weissenberg number <i>Wi</i>, solvent viscosity ratio <i>β</i>, anisotropy parameter <i>α</i>, relaxation time ratio <i>γ</i> and molecular chain arm number <i>Q</i> on the flow process are analyzed in depth. For the viscoelastic Poiseuille flow, the bigger the value of <i>Re</i>, <i>Wi</i>, and <i>α</i>, the larger the steady-state velocity is; the larger the value of <i>γ</i> and <i>Q</i>, the smaller the steady-state velocity is; the larger the value of<i> β</i>, the weaker the velocity overshoot is, but it does not affect the steady-state velocity. For the viscoelastic droplet problem, the larger the value of <i>Re</i> and <i>Wi</i>, the faster the droplet spreads; the larger the value of <i>β</i>, the weaker the droplet shrinkage behavior is, but it does not affect the final spreading width of droplet; the larger the value of <i>α</i>, the larger the droplet’s spreading width is; the larger the value of<i> γ</i> is, the stronger the droplet shrinkage behavior is; the larger the value of <i>Q</i>, the weaker its influence on the droplet’s spread width is. The improved SPH method in this paper can effectively describe the complex rheological properties and the free surface variation characteristics of viscoelastic fluid based on XPP model.

Numerical investigation on the impingement of spraying jet by an improved smoothed particle hydrodynamics method

An improved smoothed particle hydrodynamics (SPH) method for simulating the high-velocity impingement of compressible jet flow is implemented. This improved SPH method proposes a treatment to restrict the undesired density dissipation in a specific case. In this research, a utility boundary treatment is proposed to simplify the assumption process of the particles approaching the solid boundary, and the principles of the equations employed in the simulation are illustrated in detail. A free surface condition considering the density and kernel function is employed to describe the gas jet accurately. Based on the improved SPH method we discussed, the case of a spraying jet impinging on a solid wall is simulated. The influence of the neglect of the surrounding particles is discussed. It is demonstrated that a closer distance near the free surface of fluid flow will lead to obvious decay of the density and pressure, the presented SPH method provides a reasonable approach to estimate the fluid characters when the amount of calculation is huge and the neglect of surrounding material is necessary.

An improved smoothed particle hydrodynamics method for simulating crack propagation and coalescence in brittle fracture of rock materials

A new meshless numerical method, namely the improved smoothed particle hydrodynamics (ISPH) method, is proposed to simulate the fracture process of rock samples with pre-existing flaws under uniaxial compression. By improving the kernel function of SPH method, the brittle fracture characteristics of materials are presented. In ISPH, a prefabricated node segment (PNS) method is used to generate arbitrarily complex flaws, which avoids the division and distortion of traditional particles. In order to further improve the numerical accuracy, a new solid boundary treatment method called coupled dynamic buffer SBT algorithm is applied to ISPH, which is verified to be effective and robust via two benchmark samples. The effect of the length of a pre-existing flaw on the fracture mode and compressive strength of the rock sample is studied by using the elastic-brittle constitutive model. The numerical prediction results are in good agreement with the experimental observations. In addition, the effect of the unconnected rate on the crack propagation and coalescence mode of a rock sample with two pre-existing flaws under uniaxial compression is also studied. The numerical simulation results are in good agreement with the experimental results, which further verify the accuracy and superiority of the ISPH method.

Simulation of Polymer Melt Injection Molding Filling Flow Based on an Improved SPH Method with Modified Low‐Dissipation Riemann Solver

AbstractSimulations are performed for the polymer melt injection molding filling flow using an improved SPH (smoothed particle hydrodynamics) method. For improving the numerical stability of the high‐pressure and high‐viscosity injection molding filling simulation, a modified low‐dissipation Riemann solver is proposed, and the Tait equation of state and several improvements are adopted in the improved SPH method. Simulations with three cavities are performed for verification of the SPH method, including a simple long rectangular cavity and two relatively complex cavities for study of injection flow balancing. For each cavity, the pressure and velocity results of the injection molding filling simulation are demonstrated, discussed, and compared with the results of the corresponding Moldflow simulation. Furthermore, results of particle motion tracking are also analyzed for an insight into the fountain flow effect. The SPH simulation results indicate that the improved SPH method can well weaken the non‐physical pressure oscillation with reasonable pressure results and controlled melt compressibility, and the SPH results are in good agreement with the Moldflow results.

An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling

An Improved Smoothed Particle Hydrodynamics Method and Its Application in Rock Hydraulic Fracture Modelling

Smooth particle hydrodynamics simulation of dam-break impacting different obstacles

Aiming at the problems of smoothed particle hydrodynamics (SPH) method boundary imposing difficulties and particles easily penetrating solid walls, an improved complex boundary processing method is proposed. First, the improved SPH method is applied to numerically simulate the dam-break flow problem, and the numerical results are compared with the experimental results to verify the effectiveness of the method; then, the flux is added to the continuity equation to improve the pressure; finally, Numerical simulation is carried out to study the flow state of the dam-break water under different conditions of impacting on different obstacles, and the obstacles are considered as columnar, columnar with holes, wedge-shaped, semi-circular, 1/4 lower right circle obstacles and 1/4 upper right circle obstacles. The results show that: the stable pressure field can be obtained by adding flux; the improved boundary treatment method can effectively prevent particles from penetrating the solid wall, which is suitable for any complex boundary; SPH method has significant advantages in dealing with strongly nonlinear extreme deformation flow problems such as dam-break.

Numerical Simulation on the Whole Sinking Process of Open Caisson with an Improved SPH Method

The phenomena of dynamic change in the material interfaces and mechanical properties are often involved in the caisson construction. Using conventional methods to simulate these phenomena is quite difficult due to the extremely large deformation. In this study, we proposed an improved soil-water-caisson interaction algorithm with the method of smoothed-particle hydrodynamics (SPH). This algorithm dealt with the support domain truncation of the particles near the blade and applied δ − SPH to avoid the pressure fluctuation. Meanwhile, the application of dynamic particles birth and death method could simulate the whole sinking process of an open caisson with underwater soil excavation. According to the comparison between SPH simulation and centrifuge test, the distribution of sidewall effective soil pressure was consistent, which indicated promising applicability of the algorithm. It should be noted that the considerable excess pore water pressure appeared in the surrounding soil under the blade. With the dissipation of the pressure over time, the effective soil stress increased correspondingly, and it would lead to the increasing difficulty of the sinking process. Therefore, the caisson should be avoided to stop for a long time during the sinking process or it would cause the stagnation of sinking. This algorithm could simulate engineering problems involving underwater construction effectively and provide theoretical and technical support for underwater excavation, shield tunneling, and other engineering problems.

Meshless SPH analysis for transient heat conduction in the functionally graded structures

Transient heat conduction analysis of the functionally graded structures is of great importance for the structure design and manufacturing. In this study, 2D heat conduction problem is solved by the meshless smoothed particle hydrodynamics (SPH) method. To improve the computational accuracy and efficiency of traditional SPH method, a symmetric SPH approach is adopted, which can calculate a function and its derivatives of higher order using one symmetric matrix. The heat conduction function is discretized by the improved SPH method, as well as the boundary conditions. The SPH analysis of the heat conduction in several functionally graded structures with different geometries is performed and validated by the analytical values and the FEM results in literature. The effect of the graded index on the temperature distribution in the structure domain is also studied. The present paper provides an alternative potential method for the heat conduction analysis of functionally graded materials.

Numerical simulation of fluid–structure interaction with SPH method

Smoothed particle hydrodynamics (SPH) is a meshfree, Lagrangian, particle method, which combines the advantages of Euler and Lagrangian method and has special advantages in simulating violent non-linear fluid–structure interaction problems. In this study, an improved SPH method is used to simulate four fluid–structure interaction cases. Firstly, the violent flow in the mould filling process is simulated to validate that the SPH model can obtain accurate flow patterns with any complex solid boundaries. Secondly, the dam-break flow against a vertical wall is simulated, and the pressure curves are compared with the experiment. Then liquid sloshing problems under different external excitations are simulated, and the complex coupling characteristics can be captured. Finally, the interactions between fluid and floating bodies are researched. The obtained numerical results show good agreement with the results from other sources, and clearly demonstrate the effectiveness of the presented SPH method in modelling fluid–structure interaction problems.

SPH simulations on water entry characteristics of a re-entry capsule

Smoothed particle hydrodynamics (SPH) is adopted to simulate the peak impact load, the water entry process and the water entry characteristics of a re-entry capsule with the complex capsule motions modelled by a developed six degrees of freedom fluid-solid coupling model. Diffused particle distribution is developed and used in the simulations to decrease memory and computational cost. The results show that the six degrees of freedom model and diffused particle distribution are valid. The results obtained by the improved SPH method match well with experimental results, and the maximal impact load of the capsule may reach more than 10 G, even tens of G. In addition, the peak impact loads are significantly affected by the capsule vertical velocity, the capsule mass, and the pitch angle, while are slightly affected by the horizontal velocity. More concretely, the peak impact load increases with the increase of vertical velocity, and decreases with the increase of mass. However, there is no definite law between the peak load and the pitch angle. These results can provide a foundation for guiding capsule design.

A CUDA-based implementation of an improved SPH method on GPU

We present a CUDA-based parallel implementation on GPU architecture of a modified version of the Smoothed Particle Hydrodynamics (SPH) method. This modified formulation exploits a strategy based on the Taylor series expansion, which simultaneously improves the approximation of a function and its derivatives with respect to the standard formulation. The improvement in accuracy comes at the cost of an additional computational effort. The computational demand becomes increasingly crucial as problem size increases but can be addressed by employing fast summations in a parallel computational scheme. The experimental analysis showed that our parallel implementation significantly reduces the runtime, when compared to the CPU-based implementation.