Traditional Smoothed Particle Hydrodynamics Method Research Articles

An improved algorithm for Finite Particle Method considering Lagrange-type remainder

The Finite Particle Method (FPM) is a significant improvement to the traditional Smoothed Particle Hydrodynamics method (SPH), which can greatly improve the computational accuracy of the entire computational domain. However, unstable calculation results and long computational time are still major obstacles to the development of FPM. Based on matrix decomposition, the fundamental equations of the traditional Finite Particle Method are rewritten and a Generalized Finite Particle Method (GFPM) is derived by introducing Lagrange-type remainder. By deriving and rewriting the fundamental equations, the GFPM method can be theoretically proven to be always stable. Numerical examples show that the GFPM method can utilize a smaller computational scale to achieve the same computational accuracy as the FPM method, with a corresponding reduction in computational time. Finally, the GFPM method is applied to a one-dimensional stress wave propagation problem and a one-dimensional heat conduction problem, and the computational results are compared with those of the SPH method and the FPM method, which verify that the GFPM has higher computational accuracy and stability.

Research on the Water Entry of the Fuselage Cylindrical Structure Based on the Improved SPH Model

During aircraft landing on water, the intense impact load may lead to significant local deformation of the fuselage skin. Ensuring the aircraft’s integrity and reliability is of paramount importance. This paper investigates the fuselage skin’s dynamic response during water entry. In the simulation of complex water entry problems, the smoothed particle hydrodynamics (SPH) method can fully leverage the advantages of the particle method. However, the traditional SPH method still suffers from the drawbacks of tensile instability, significantly affecting the computational accuracy. Therefore, this paper first introduces the improved SPH model addressing fluid and solid tensile instability issues. Furthermore, the Riemann-based contact algorithm at the fluid–solid interface is also demonstrated. Based on the above improved SPH model, the simulation of water entry of the elastic cylinder is performed to validate the efficacy of the improved SPH model. Then, the dynamic response characteristics of elastic fuselage skin and the skin–stringer–floor–column structure when it enters the water are analyzed, including the deformation features and slamming force. Lastly, based on the presented damage model, a study is conducted on the water entry of the metallic elastic–plastic skin–stringer–floor–column structure, analyzing the locations of failure and providing guidance for the structural safety design of engineering.

An improved SPH scheme for the 3D FEI (Fluid-Elastomer Interaction) problem of aircraft tire spray

The problem of aircraft tire spray produced by taking off or landing on wet runways is widely concerned. When simulating this kind of FEI(Fluid-Elastomer Interaction) problem with traditional SPH((Smoothed Particle Hydrodynamics) method, there are some drawbacks in both fluid and elastomer calculation. For the elastomer simulation, the TL-SPH(Total Lagrangian-SPH) is used to deal with the deformation of tire under complicated motion and load. For the fluid simulation, a new SPH scheme of Riemann solver combined with transport velocity is proposed to solve the problem of particle clumping when the free surface is suffering from violent splash. Then the tire spray model by unified SPH is established, in which both the tire deformation and the spray pattern are validated by experiments. Finally, based on the large-scale tire spray simulation, the phenomenon of tire hydroplaning is studied.

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.

Simulating multi-phase sloshing flows with the SPH method

In this paper, the intense sloshing flow is simulated by Smoothed Particle Hydrodynamics (SPH) method successfully. First, the traditional SPH method is used for the simulation of sloshing process; and the obtained results for free surface shape and pressure evolution are in good agreement with the experimental data. Then, the δ-SPH method and particle shifting technique (PST) are introduced in the traditional SPH model to improve its stability and accuracy in simulating sloshing flow. Air phase does have an inescapable influence on water phase in intense sloshing process. Thus, an improved multiphase SPH model with pressure correction algorithm is utilized for interfacial sloshing simulation. The stability, accuracy and conservation of pressure correction algorithm are validated by the cases of hydrostatic test and dam breaking test. Besides, the comparison results show that unphysical pressure transmission at the interface between two fluids with large density ratio is effectively suppressed. Finally, the effect of air is considered in the multiphase flow simulation of sloshing process with presented multiphase δ-SPH and pressure correction utilized. The phenomenon that air phase is involved into inner water flow and then moves, rolls and rises in it is replicated accurately. It is found that both the shape of free surface and the air cavities during the slamming phase are well captured, which proves that the integrated multiphase SPH is effectively utilized for the simulation of such multiphase problem as sloshing.

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.

Computation of nonlinear acoustic waves using smoothed particle hydrodynamics

A Lagrangian approach for solving nonlinear acoustic wave problems is presented with direct computation from smoothed particle hydrodynamics. The traditional smoothed particle hydrodynamics method has been applied to solve linear acoustic wave propagations. However, nonlinear acoustic problems are common in medical ultrasonography, sonic boom research, and acoustic levitation. Smoothed particle hydrodynamics is a Lagrangian meshfree particle method that shows advantages in modeling nonlinear phenomena, such as the shock tube problem, and other nonlinear problems with material separation or deformable boundaries. The method is used to solve the governing equations of fluid dynamics for simulating nonlinear acoustics. The present work also tests the method in solving the nonlinear simple wave equation based on Burgers’ equation. Effects of initial particle spacing, kernel length, and time step are then discussed based on the wave propagation simulation. Different kernel functions are also evaluated. The res...

Modeling and simulation of injection molding process of polymer melt by a robust SPH method

• A robust SPH approach was proposed. • Solid boundaries were modeled in a flexible way. • Injection molding process of polymer melt was studied. • The fluctuations-free pressure and velocity fields were recovered. In the present study, the injection molding process of polymer melt based on the generalized Newtonian fluid model is investigated by a robust smoothed particle hydrodynamics (SPH) method. The numerical method is proposed by introducing a Rusanov flux into the continuity equation to improve the prediction of the pressure distribution and employing a corrected kernel gradient to improve the computational accuracy. In addition, a robust treatment of solid boundary is presented and verified by the spin-down problem. The merits of the robust SPH method are firstly illustrated by 2D dam breaking flow. Then the numerical method is extended to deal with the flow phenomena related to injection molding process of polymer melt. A number of numerical examples including 2D injection moldings of a thin plate mold, a circular disc with core, a ring-shaped channel, and a S-shaped cavity, and 3D injection moldings of a Z-shaped cavity and a four-legged fork are conducted. The numerical results are in agreement with the experiments, which demonstrate that the SPH method proposed here is capable of handling with injection molding process of polymer melt in a robust manner. Moreover, the robust SPH method allows to recover the fluctuations-free pressure and velocity fields which in most cases cannot be easily obtained by the traditional SPH method.

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) method reduces the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed, to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics.

Numerical Simulation of Violent Impinging Jet Flows with Improved SPH Method

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for simulating violent water impinging jet flow problems. The presented SPH method involves three major modifications on the traditional SPH method, (1) The kernel gradient correction (KGC) and density correction are used to improve the computational accuracy and obtain smoothed pressure field, (2) a coupled dynamic solid boundary treatment (SBT) is used to remove the numerical oscillation near the solid boundary and ensure no penetration condition, (3) a free surface condition, which is obtained from the summation of kernel function and volume, is used to describe the water jet accurately. Different cases about violent impinging jet flows are simulated. The influences of impact velocity and angles are investigated. It is demonstrated that the presented SPH method has very good performance with accurate impinging jet patterns and pressure field distribution. It is also found that the pressure time histories of observation points are greatly influenced by the rarefaction wave from surrounding air. Closer distance from free surface can lead to quicker decay of the pressure time history.

An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field.

Simulation of polymer filling process by an improved smoothed particle hydrodynamics method based on higher-order Taylor expansion

In this work, an improved smoothed particle hydrodynamics (SPH) method based on higher order Taylor expansion (CSPH_HT) is proposed and tentatively applied to the filling process of the viscoelastic fluid. Owing to the disadvantages of the traditional SPH method and the presented corrected SPH methods, the CSPH_HT method based on the higher order Taylor expansion is proposed and described in detail. In order to illustrate the validity and merits of the CSPH_HT method, two benchmark problems are simulated and discussed. The numerical results show that the proposed CSPH_HT method has higher numerical accuracy and better stability. Subsequently, the proposed improved SPH method is extended to simulate the filling processes of the viscoelastic fluid in the ring-shaped mold, for the purpose of exhibiting the capacity of the proposed method. The extended pom-pom (XPP) model and finitely extensible nonlinear elastic-Peterlin (FENE-P) model fluid are all considered in this case, in which the viscoelastic fluid flow and extra stress are shown. The differences in fluid flow between the XPP model and FENE-P model are also discussed. Finally, the filling process of the viscoelastic fluid in the square mold with single inlet or two inlets are tentatively simulated. The differences between the filling process of XPP fluid and the filling process of FENE-P fluid are shown, and the influences of the parameters of the mold on the flow are analyzed. Especially, the influences of locations and sizes of two inlets on the filling process of viscoelastic fluid are illustrated. The XPP model fluid and FENE-P model fluid show different characteristics in the filling process and small change of the size of the mold can lead to obvious change of the flow.

Numerical simulation on oscillation of micro-drops by means of smoothed particle hydrodynamics

In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. SPH is a Lagrangian meshfree particle method, and it is attractive in dealing with free surfaces, moving interfaces, and deformable boundaries. The improved SPH method modifies the kernel gradient in the traditional SPH method with a new kernel function and a modified SPH discrete form. Use of improved smoothed particle hydrodynamics is made to carry out numerical analysis on micro liquid drop oscillation process. The study focuses on the relation between the micro liquid drop oscillation damping and the oscillating period and amplitude in different aspect ratio and Re number. It is shown that for the micro liquid drop oscillation process with aspect ratio λ≤ 4, under the circumstance of constancy of other parameters, the larger the Re number, the more intense the change of liquid drop's shapes, the weaker the damping effect, and the longer the period of liquid drop's oscillation. Under the circumstance of constancy of Re number, as the initial aspect ratio of liquid drop increases, the amplitude of liquid drop oscillation is stronger, and the period of liquid drop's oscillation is longer.

A Corrected Incompressible SPH Method for Fixed Body Wave Impact Simulation

The smoothed particle hydrodynamics method (SPH) are emerging as potential tools for studying water wave related problems, in particular those with a rapidly moving free surface. And the incompressible smoothed particle hydrodynamics (ISPH) method has been shown to be accurate and stable for many problems than the traditional SPH by many papers in literature. In this study, the cases about wave breaking and solitary wave are simulated. Their results are compared with available analytical, experimental, and other numerical data found in literatures and reasonably good agreement is achieved. And the corrected incompressible smoothed particle hydrodynamics has been shown to be useful for simulating fixed body wave impact.

Simulate Wave Body Interaction Based on the Incompressible SPH Method

The smoothed particle hydrodynamics method (SPH) has been proved to have an excellent ability in dealing with issues related to the wave. Compared with the SPH method, the incompressible smoothed particle hydrodynamics (ISPH) method has solved the pressure by solving the Poisson equation, rather than by solving the equation of state. The ISPH method presents a good approach to capture the free surface particle. With the respect of the SPH method, the ISPH method shows more stability and accurate of the numerical results than the traditional SPH method. This paper presents an ISPH method for two dimensional wave-body coupled problems, especially for the move structure. In most conventional ISPH techniques, the boundary is fixed; in this work, the move boundary is applied in the ISPH method. Then the model is applied to two problems: (1) interaction between a fixed rectangular structure and a liner wave; (2) two dimensional floating rectangular structure coupled with the nonlinear wave. The final results show agreement with the experiment data and phenomena.

An Efficient SPH Approach for Nearly Incompressible Fluid Simulation

In this paper, we present an efficient approach based on Smoothed Particle Hydrodynamics (SPH) to simulate nearly incompressible fluids. The proposed method is an extension of the traditional SPH method designed for compressible fluids. We first introduce a new scheme for pressure evaluation to satisfy the incompressibility constraints. Then novel calculation methods for pressure force and viscosity force are discussed. Finally, the results demonstrate that our method is more capable of realistically simulating fluids with near-incompressibility than previous method.

A corrected smoothed particle hydrodynamics approach to solve the non-isothermal non-Newtonian viscous fluid flow problems

In this paper, a corrected smoothed particle hydrodynamics (SPH) method is proposed to solve the problems of non-isothermal non-Newtonian viscous fluid. The proposed particle method is based on the corrected kernel derivative scheme under no kernel derivative and incompressible conditions, which possesses higher accuracy and better stability than the traditional SPH method. Meanwhile, a temperature-discretization scheme is deduced by the concept of SPH method for the purpose of precisely describing the evolutionary process of the temperature field. Reliability of the corrected SPH method for simulating the non-Newtonian viscous fluid flow is demonstrated by simulating the isothermal Poiseuille flow and the jet fluid of filling process; and the validity and accuracy of the proposed SPH discrete scheme in a temperature model for solving the non-isothermal fluid flow are tested by solving the non-isothermal Couette flow and 4:1 contraction flow. Subsequently, the proposed corrected SPH method combined with the SPH temperature-discretization scheme is tentatively extended to include the simulation of the non-isothermal non-Newtonian viscous free-surface flows in the ring-shaped and C-shaped cavities. Especially, the convergence of numerical simulations is analyzed, and the influences of heat flow parameters on the temperature and fluid flow at different positions are discussed.

Theoretical analysis on the applicability of traditional SPH method

As a fully Lagrangian, particle-based numerical method, the traditional smoothed particle hydrodynamics (SPH) generally suffers from the accuracy problem. To investigate the physical origins of this numerical error, the elastic effect between SPH particles is specifically identified by analogy with physical entities, and a unique non-dimensional number is proposed to evaluate the relative dominance of viscous to elastic effect. Through the simulation of two-dimensional Couette flow, the velocity profile and arrangement of particles are examined for various ratios of viscous to elastic effect. The effective viscosity of SPH particles decreases as this non-dimensional number increases, while the increase of particle number significantly reduces the effective viscosity only at lower ratio of viscous to elastic effect. The disparity among nominal viscous dissipation, total dissipation, and theoretical dissipation further confirms the presence of unphysical dissipation resulting from the elastic effect. In summary, due to the constraints from the Mach number and the ratio of viscous to elastic effect, there exists a critical Reynolds number below which the Newtonian behavior could be approximately obtained through suitable choice of model parameters.

A robust shell element in meshfree SPH method

With the incorporation of total Lagrangian smoothed particle hydrodynamics (SPH) method equation and moving least square (MLS) function, the traditional SPH method is improved regarding the stability and consistency. Based on Mindlin-Ressiner plate theory, the SPH method simulating dynamic behavior via one layer of particles is applied to plate’s mid-plane, i.e., a SPH shell model is constructed. Finally, through comparative analyses on the dynamic response of square, stiffened shells and cylindrical shells under various strong impact loads with common finite element software, the feasibility, validity and numerical accuracy of the SPH shell method are verified. Consequently, further researches on SPH shell may well pave the way towards solving problems involving dynamic plastic damage, tearing or even crushing.

IMPROVED SMOOTHED PARTICLE HYDRODYNAMICS WITH RANS FOR FREE-SURFACE FLOW PROBLEMS

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for numerical simulation of free-surface flow problems. The presented SPH method involves two major modifications on the traditional SPH method: (1) kernel gradient correction (KGC) and density correction to improve the computational accuracy in particle approximation and (2) RANS turbulence model to capture the inherent physics of flow turbulence. In the simulation, artificial compressibility for modeling incompressible fluid and ghost particles for treating solid boundaries are both applied. The presented SPH has been applied to two dam-breaking problems. We demonstrated that the presented SPH method has very good performance with more accurate flow patterns and pressure field distribution.