Standard Smoothed Particle Hydrodynamics Research Articles

A Dual-Particle Approach for Incompressible SPH Fluids

Tensile instability is one of the major obstacles to particle methods in fluid simulation, which would cause particles to clump in pairs under tension and prevent fluid simulation to generate small-scale thin features. To address this issue, previous particle methods either use a background pressure or a finite difference scheme to alleviate the particle clustering artifacts, yet still fail to produce small-scale thin features in free-surface flows. In this article, we propose a dual-particle approach for simulating incompressible fluids. Our approach involves incorporating supplementary virtual particles designed to capture and store particle pressures. These pressure samples undergo systematic redistribution at each time step, grounded in the initial positions of the fluid particles. By doing so, we effectively reduce tensile instability in standard SPH by narrowing down the unstable regions for particles experiencing tensile stress. As a result, we can accurately simulate free-surface flows with rich small-scale thin features, such as droplets, streamlines, and sheets, as demonstrated by experimental results.

SPH implementation of a critical state-based hypoplastic model for granular materials in large-deformation problems

In this work, an advanced hypoplastic model incorporating the critical state is integrated into smoothed particle hydrodynamics (SPH) for numerical investigation of problems with large deformation. This numerical method performs well in cases of element tests such as oedometer test, simple shear test and plain strain compression test, which usually own regular velocity fields. However, the standard SPH implementation will generate significant stress drift away from the failure surface in more complex geotechnical problems featured with dramatically-varying velocity field. This unrealistic stress state may deteriorate the stress state with a further step. As a result, a vicious circle takes place, which could give rise to a calculation failure. With this regard, a return mapping strategy is proposed to regulate the stress state locating beyond the failure surface. To this end, a closed-form solution to predicting the failure surface implicitly incorporated in the hypoplastic model is derived. Finally, the capability of the proposed numerical method is examined with two classical benchmark problems for granular materials, including the sand column collapse and rigid footing by comparing the numerical results with those from experiments and theoretical solutions.

Volume conservation issue within SPH models for long-time simulations of violent free-surface flows

Smoothed Particle Hydrodynamics (SPH) simulations of violent sloshing flows characterized by a strong fragmentation of free-surface can be affected by volume conservation errors. These errors can accumulate in time and preclude the possibility of using such models for long-time simulations. In the present work, different techniques to measure directly the particles’ volumes by their positions are displayed. Thanks to these algorithms, we discussed how volume errors develop when introducing stabilization terms in the standard SPH schemes. Further, we show that the control of these errors can be achieved through two different (non-alternative) stabilization terms: (i) enforcement of dynamic boundary conditions on thin fluid jets and drops; and (ii) a dynamical switch that can impose or not the time variation of the particle masses.To demonstrate the effectiveness of the numerical techniques, four different violent sloshing flows are investigated and compared with experimental data.

Direct numerical simulation of three-dimensional isotropic turbulence with smoothed particle hydrodynamics

This study presents an investigation of the capability of smoothed particle hydrodynamics (SPH) to simulate three-dimensional isotropic turbulence. The effect of the error introduced by the particle disorder is assessed by comparing the standard Lagrangian SPH with an Eulerian adaptation. For the free decay of isotropic turbulence in a triple periodic box, the Eulerian SPH shows very good agreement with the reference solution, while the particle disorder in Lagrangian simulations yields an incorrect prediction of turbulent energy spectra. For the first time, a SPH investigation on linearly forced isotropic turbulence is also conducted with a focus on how the numerical dissipation affects the obtained solution. It is found that by using a Godunov-type SPH scheme for the continuity equation and by employing Roe's approximate solver for the Riemann problem at the interface of each neighboring particle, a stable solution is obtained, which is also in agreement with the results predicted by the theory of homogeneous isotropic turbulence. The efficacy of the particle shifting technique applied to turbulent SPH flows is studied in the end. Numerical findings indicate that corrective terms derived from the arbitrary Lagrangian–Eulerian theory are essential for a proper estimation of turbulence characteristics.

An essentially non-hourglass formulation for total Lagrangian smoothed particle hydrodynamics

The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic solid dynamics suffers from hourglass modes which can grow and lead to the failure of simulation for problems with large deformation. To address this long-standing issue, we present an essentially non-hourglass formulation based on volumetric-deviatoric stress decomposition. Inspired by the fact that the artifact of nonphysical zigzag particle distribution induced by the hourglass modes is mainly characterized by shear deformation and the standard SPH discretization for the viscous term in the Navier–Stokes (NS) equation, the present formulation computes the action of shear stress directly through the Laplacian of displacement other than from the divergence of shear stress. A comprehensive set of challenging benchmark cases are simulated to demonstrate that, while improving accuracy and computational efficiency, the present formulation is able to essentially suppress the hourglass modes and achieves very good numerical stability with a single general effective parameter. In addition, the deformation of a practically relevant stent structure is simulated to demonstrate the potential of the present method in the field of biomechanics.

Generalized coordinate smoothed particle hydrodynamics with an overset method in total Lagrangian formulation

AbstractThis study proposes a generalized coordinate smoothed particle hydrodynamics (GCSPH) method coupled with an overset method using the total Lagrangian formulation for solving large deformation and crack propagation problems. In GCSPH, the physical space is decomposed into multiple domains, each of which is mapped to a generalized space to avoid coordinate singularities as well as to flexibly change the spatial resolution. The SPH particles are then non‐uniformly distributed in the physical space (e.g., typically in a boundary‐conforming manner) and defined uniformly in each generalized space, similar to the standard SPH. The SPH particles in the generalized and physical spaces are numerically related by coordinate transformation matrices. The use of non‐uniform particle distributions decreases the total number of particles, thus significantly reducing the simulation cost. Three numerical cases: three‐dimensional brittle crack propagation, Taylor impact, and plugging failure, are presented to validate the proposed method. The numerical results are sufficiently accurate compared with the standard total Lagrangian SPH. Furthermore, these results also show the benefits of GCSPH, which not only effectively reduces the computational cost but also eliminates the effects of particle arrangement. These advantages allow GCSPH to perform high‐resolution three‐dimensional problems, which are otherwise costly to perform with the standard SPH.

Study of the weakly-compressible SPH method for improving pressure distribution of violent fluid-structure impact flows

Abstract When a traditional Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) model is used to simulate free surface flow with a large Reynolds number, an unstable numerical calculation due to high random pressure oscillations will result, while an accurate pressure field is of vital significance for simulating violent fluid-structure interactions. Riemann-based SPH and Delta-SPH are widely used to solve this problem. In this paper, to enhance computational efficiency, the SPH method is implemented on a General Processing Unit (GPU) platform using Compute Unified Device Architecture (CUDA). Parallelized SPH programs including the standard SPH method, Riemann-based SPH and Delta-SPH are verified by a dam break model with large Reynolds number and violent deformation of free surfaces. The results show that all SPH methods can vividly reflect the whole process of splashing, rolling and backward jet flow; both the Riemann-based SPH and the Delta-SPH methods are effective in alleviating the problem of inhomogeneous pressure distribution in the simulation process; the Riemann-based SPH method has better stability even with relatively large particle spacing, and it has higher accuracy in simulating impact pressure. When the number of particles reaches 100,000, compared with a single-thread Central Processing Unit (CPU) implementation, the speedups obtained with NVIDIA Titan V with high computing cores and Quadro K2200 with low computing cores are thousands and hundreds, respectively.

Large Scale Hydrodynamically Coupled Brownian Dynamics Simulations of Polymer Solutions Flowing through Porous Media.

Large scale simulations of polymer flow through porous media provide an important tool for solving problems in enhanced oil recovery, polymer processing and biological applications. In order to include the effects of a wide range of velocity and density fluctuations, we base our work on a coarse-grain particle-based model consisting of polymers following Brownian dynamics coupled to a background fluid flow through momentum conserving interactions. The polymers are represented as Finitely Extensible Non-Linear Elastic (FENE) dumbbells with interactions including slowly decaying transient forces to properly describe dynamic effects of the eliminated degrees of freedom. Model porous media are constructed from arrays of parallel solid beams with circular or square cross-sections, arranged periodically in the plane perpendicular to their axis. No-slip boundary conditions at the solid–fluid interfaces are imposed through interactions with artificial particles embedded within the solid part of the system. We compare the results of our simulations with those of standard Smoothed Particle Hydrodynamics simulations for Newtonian flow through the same porous media. We observe that in all cases the concentration of polymers at steady state is not uniform even though we start the simulations with a uniform polymer concentration, which is indicative of shear-induced cross-flow migration. Furthermore, we see the characteristic flattening of the velocity profile experimentally observed for shear-thinning polymer solutions flowing through channels as opposed to the parabolic Poiseuille flow profile for Newtonian fluids.

An improved smoothed particle hydrodynamics approach using new inverse kernel function

The main limitation of Smoothed Particle Hydrodynamics (SPH) method that resists the method's potential is its lack of providing stability and accuracy to the numerical technique. We improve the accuracy of the standard SPH technique, by formulating a new inverse logarithmic kernel function. This new kernel function is derived based on the underlying properties of kernel functions. The approximation technique used here is based on the Moving Least Squares based technique. The adequacy of the proposed kernel function is tested by simulation of 2D shock wave propagation and 3D dam-break free surface flow against a cuboidal obstacle. The method was validated against experimental data by Kleefsman et al., [1]. The numerical results reveal that our new SPH approach using inverse logarithmic kernel function outperforms existing ones in particle restoration, zero error, better accuracy and enhanced efficiency in kernel approximation. This new kernel function showed some improvement over existing kernels by showing very less error approximation value of 0.035h2. The results showed some improvements over standard technique by being capable of handling problems with large deformations accurately and precisely.

An improved thermal model for SPH metal cutting simulations on GPU

This paper presents the first application of a higher-order Smoothed Particle Hydrodynamics (SPH) method to the thermal modeling of metal cutting problems. With this application, the heat transfer equation in the thermo-mechanical simulation of metal cutting is solved more accurately by addressing the consistency issue of standard SPH formulations. Furthermore, through a robust and effective surface-detection algorithm, this work enables the SPH cutting models to include heat loss thermal boundary conditions for the first time. Process forces, tool temperatures, and chip geometry are numerically investigated in machining a Ti6Al4V workpiece at two different cutting speeds. Several validation tests and sensitivity analyses are performed in high resolution, thanks to the runtime acceleration of SPH by parallel computing on Graphics Processing Units (GPUs). The results show that SPH simulations with the proposed thermal modeling approach achieve more realistic serrated chips in titanium cutting problems.

A Mindlin shell model based on the corrective smoothed particle method and accuracy implementation of the free boundary

A meshless shell method for large deformation and a linear relation between the Cauchy stress tensor and the Almansi strain tensor based on the corrective smoothed particle method (CSPM) is presented in this paper. Due to the use of the shell theory, only one layer of particles in the reference plane is required to discretize the shell model. The CSPM combining the kernel estimate with the Taylor series expansion is adopted, which resolves the general problems of low precision and particle deficiency in standard smoothed particle hydrodynamics (SPH). The discrete governing equations of the shell in the strong form are derived using the conservation condition and the CSPM interpolation function. Aiming at the sore point of the free boundary in the meshless method, the developed model enables the modified governing equations to automatically satisfy the free boundary condition without additional treatment. Moreover, the total Lagrangian kernel function and stress points are employed to eliminate tensile instability and instability induced by the rank deficiency. Finally, several numerical examples are used to verify the validity and accuracy of the meshless shell model.

Generalized entropically damped artificial compressibility for weakly compressible SPH

This paper presents a formulation of a general form of an equation for pressure using thermodynamic principles. The motivation for this is in large part due to the need for a pressure equation for smoothed particle hydrodynamics, SPH, that takes into account the role of entropy. This is necessary because the use of physical and artificial viscosity leads to an increase in entropy. While such an increase in entropy in liquids may be negligibly small, standard SPH formulations treat a liquid as a weakly compressible gas. Consequently, for fluid–fluid and fluid–structure impact flows, the resulting increase in entropy is not negligible anymore. The proposed pressure equation contains diffusion terms whose main role is to smooth out unphysically large numerical oscillations in the pressure field related to the shock during an impact event. One consequence of adopting this numerical scheme, however, is that there are new (free) parameters that must be set. Nevertheless, effort has been made to obtain their plausible estimators from physical principles. The proposed model is also applicable outside the domain of SPH.

SPH crowds: Agent-based crowd simulation up to extreme densities using fluid dynamics

In highly dense crowds of humans, collisions between people occur often. It is common to simulate such a crowd as one fluid-like entity (macroscopic), and not as a set of individuals (microscopic, agent-based). Agent-based simulations are preferred for lower densities because they preserve the properties of individual people. However, their collision handling is too simplistic for extreme-density crowds. Therefore, neither paradigm is ideal for all possible densities.In this paper, we combine agent-based crowd simulation with Smoothed Particle Hydrodynamics (SPH), a particle-based method that is popular for fluid simulation. We integrate SPH into the crowd simulation loop by treating each agent as a fluid particle. The forces of SPH (for pressure and viscosity) then augment the usual navigation behavior and contact forces per agent. We extend the standard SPH model with a dynamic rest density per particle, which intuitively controls the crowd density that an agent is willing to accept. We also present a simple way to let agents blend between individual navigation and fluid-like interactions depending on the SPH density.Experiments show that SPH improves agent-based simulation in several ways: better stability at high densities, more intuitive control over the crowd density, and easier replication of wave-propagation effects. Also, density-based blending between collision avoidance and SPH improves the simulation of mixed-density scenarios. Our implementation can simulate tens of thousands of agents in real-time. As such, this work successfully prepares the agent-based paradigm for crowd simulation at all densities.

Towards pseudo-spectral incompressible smoothed particle hydrodynamics (ISPH)

In this paper a pseudo-spectral incompressible smoothed particle hydrodynamics (FFT-ISPH) solver is presented. While the solution of the linear system arising from the pressure Poisson equation in physical space using iterative solvers in incompressible SPH is a viable solution, it is widely accepted that the computational cost of solving the pressure Poisson equation by iterative solvers is excessive and affects negatively on the efficiency of the solver. The proposed scheme is an intermediate between a fully spectral and a standard incompressible SPH solver. Herein, the solution of the pressure Poisson equation is performed in spectral space whereas the discretisation and time integration are performed in physical space. This results in a second and higher-order scheme with the classical first-order projection and a third-order Runge-Kutta time integration scheme, respectively. A detailed performance analysis shows gains in computational cost of two orders of magnitude. Further, it is demonstrated that the solution of the pressure Poisson equation in spectral space is independent of the number of neighbouring nodes, in contrast to the iterative solver whose cost increases by a factor of three with smoothing length to particle size ratio. Periodic, bounded, and mixed boundary conditions test cases have been used to demonstrate the applicability, accuracy and robustness of the scheme with second and fourth-order convergence rates. The scheme opens an avenue for simulations of high-order incompressible flows in SPH where filtering operations in the frequency domain can be performed straightforwardly.

A three-dimensional beam formulation for large deformation and an accurate implementation of the free boundary

This paper presents a meshless model for quasi-static and dynamic analysis of a three-dimensional Timoshenko beam with geometric nonlinearity. A general mathematical formulation is constructed based on the corrective smoothed particle method (CSPM), which can correct the low precision and completeness deficiency of the standard smoothed particle hydrodynamics(SPH) method. The discrete governing equations as well as the boundary conditions in strong form for the three-dimensional beam are then derived by using the conservation conditions and the CSPM interpolation function. The developed model enables one to expediently discretize the geometric nonlinear beam with only a row of particles at the central axis and to automatically satisfy the free boundary condition without any additional treatment. Moreover, Lagrangian kernel function and stress points are adopted to eliminate tensile instability and instability induced by the rank deficiency within the particle methods. Finally, comparisons with several results obtained from the existing literature are provided to demonstrate the validity and potential of the present procedure.

An arbitrary Lagrangian Eulerian smoothed particle hydrodynamics (ALE-SPH) method with a boundary volume fraction formulation for fluid-structure interaction

We present a new weakly-compressible smoothed particle hydrodynamics (SPH) method capable of modeling non-slip fixed and moving wall boundary conditions. The formulation combines a boundary volume fraction (BVF) wall approach with the transport-velocity SPH method. The resulting method, named SPH-BVF, offers detection of arbitrarily shaped solid walls on-the-fly, with small computational overhead due to its local formulation. This simple framework is capable of solving problems that are difficult or infeasible for standard SPH, namely flows subject to large shear stresses or at moderate Reynolds numbers, and mass transfer in deformable boundaries. In addition, the method extends the transport-velocity formulation to reaction-diffusion transport of mass in Newtonian fluids and linear elastic solids, which is common in biological structures. Taken together, the SPH-BVF method provides a good balance of simplicity and versatility, while avoiding some of the standard obstacles associated with SPH: particle penetration at the boundaries, tension instabilities and anisotropic particle alignments, that hamper SPH from being applied to complex problems such as fluid-structure interaction in a biological system.

Simulation of contact interface between elastic solids using smoothed particle hydrodynamics

In recent years, the use of the smoothed particle hydrodynamics (SPH) method has increased. However, most researches have restricted the application of this method to the fluids field. Few publications have reported the use of SPH to study solid problems. Moreover, only a small amount of investigations have considered the interface when two solids are in contact. The standard SPH method is able to determine the interaction of two objects through mutual search of particles at the interface. Taking this into account, herein we report a new strategy named interfacial SPH for simulating the contact of elastic objects. In our simulations, the search domain only contained the particles of the object, and the interaction between the two objects was achieved by means of the interface force. First, the collision of two aluminium rectangles was simulated in order to test the usefulness of the simulation strategy at the linear interface. Later, the collision between two discs was simulated to test the strategy at the curved interface. Subsequently, the collision of two elastic rubber rings and the impact of a bullet on an elastic plate were simulated. These last two models showed how the strategy used in the present investigation can be applied for the simulation of large deformation of elastomers. Finally, this paper analysed the problems of applying the standard SPH method in the simulation of the interface contact between two solids. The XSPH method and the artificial stress method were used in our simulations to ensure simulation stability.

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.

Implicit Frictional Boundary Handling for SPH.

In this article, we present a novel method for the robust handling of static and dynamic rigid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. We build upon the ideas of the density maps approach which has been introduced recently by Koschier and Bender. They precompute the density contributions of solid boundaries and store them on a spatial grid which can be efficiently queried during runtime. This alleviates the problems of commonly used boundary particles, like bumpy surfaces and inaccurate pressure forces near boundaries. Our method is based on a similar concept but we precompute the volume contribution of the boundary geometry. This maintains all benefits of density maps but offers a variety of advantages which are demonstrated in several experiments. First, in contrast to the density maps method we can compute derivatives in the standard SPH manner by differentiating the kernel function. This results in smooth pressure forces, even for lower map resolutions, such that precomputation times and memory requirements are reduced by more than two orders of magnitude compared to density maps. Furthermore, this directly fits into the SPH concept so that volume maps can be seamlessly combined with existing SPH methods. Finally, the kernel function is not baked into the map such that the same volume map can be used with different kernels. This is especially useful when we want to incorporate common surface tension or viscosity methods that use different kernels than the fluid simulation.

3D Thermal Simulation of a Laser Drilling Process with Meshfree Methods

Numerical simulation of laser drilling is rapidly gaining interest in academia and industry since this process remains one of the most important and widely-used technologies in modern manufacturing. Meshfree methods such as Smoothed Particle Hydrodynamics (SPH) have proven to be successful as a numerical tool for the computation of the heat transfer and material removal associated with a laser drilling problem. Nonetheless, the vast majority of recent developments incorporate an inconsistent SPH kernel into their thermal simulations. In this paper, several enhanced schemes are implemented to address this problem by solving the heat transfer more accurately. These meshfree schemes can provide a second-order accurate discretization of the Laplace operator and abolish the inconsistency issue of the standard SPH kernels. An efficient approach is additionally suggested to handle the associated boundary conditions, which relies on the idea of the color function and particle label. The implementation is initially validated by a 3D benchmark study and then applied for the first time to a laser drilling problem.