Adaptive Smoothing Lengths Research Articles

SPH modeling and investigation of cold spray additive manufacturing with multi-layer multi-track powders

Cold spray (CS), as a new solid-state additive manufacturing technique, involves complex phenomena like high-speed impacting of micro-powders, large material deformations, phase change and jet generation. The CS process is difficult to be accurately simulated, and the underlying coating mechanisms, especially for multi-powders CS, have not been well understood. As a Lagrangian and particle method, the smoothed particle hydrodynamics (SPH) method has natural advantages in treating large deformations and capturing moving interfaces. In this work, we present an improved SPH approach to implement three-dimensional particle modeling and study of the multi-layer multi-track CS problem. The kernel gradient correction (KGC), adaptive smoothing length and the constitutive model are integrated in the improved SPH. The contour profile and width thickness ratio of the deformed powder obtained by the present simulation are very close to the experimental results. The bonding behaviors in a single powder CS with different materials are first explained where the critical velocities for different materials are obtained. Furthermore, coating behaviors in CS with different layers and tracks of powders are comprehensively analyzed. Some typical deformation parameters of the powders track with regard to an increasing impacting velocity are attained. With the present numerical model, a larger scale multi-layer multi-track CS is promising to be reproduced with some parameter windows predicted, which is greatly helpful to CS operations.

Adaptive smoothing length method based on weighted average of neighboring particle density for SPH fluid simulation

BackgroundIn the smoothed particle hydrodynamics (SPH) fluid simulation method, thesmoothing length affects not only the process of neighbor search but also the calculation accuracy of the pressure solver. Therefore, it plays a crucial role in ensuring the accuracy and stability of SPH. MethodsIn this study, an adaptive SPH fluid simulation method with a variable smoothing length is designed. In this method, the smoothing length is adaptively adjusted according to the ratio of the particle density to the weighted average of the density of the neighboring particles. Additionally, a neighbor search scheme and kernel function scheme are designed to solve the asymmetry problems caused by the variable smoothing length. ResultsThe simulation efficiency of the proposed algorithm is comparable to that of some classical methods, and the variance of the number of neighboring particles is reduced. Thus, the visual effect is more similar to the corresponding physical reality. ConclusionsThe precision of the interpolation calculation performed in the SPH algorithm is improved using the adaptive-smoothing length scheme; thus, the stability of the algorithm is enhanced, and a larger timestep is possible.

Parallel fast-neighbor-searching and communication strategy for particle-based methods

PurposeThis paper aims to develop a parallel fast neighbor search method and communication strategy for particle-based methods with adaptive smoothing-length on distributed-memory computing systems.Design/methodology/approachWith a multi-resolution-based hierarchical data structure, the parallel neighbor search method is developed to detect and construct ghost buffer particles, i.e. neighboring particles on remote processor nodes. To migrate ghost buffer particles among processor nodes, an undirected graph is established to characterize the sparse data communication relation and is dynamically recomposed. By the introduction of an edge coloring algorithm from graph theory, the complex sparse data exchange can be accomplished within optimized frequency. For each communication substep, only efficient nonblocking point-to-point communication is involved.FindingsTwo demonstration scenarios are considered: fluid dynamics based on smoothed-particle hydrodynamics with adaptive smoothing-length and a recently proposed physics-motivated partitioning method [Fu et al., JCP 341 (2017): 447-473]. Several new concepts are introduced to recast the partitioning method into a parallel version. A set of numerical experiments is conducted to demonstrate the performance and potential of the proposed parallel algorithms.Originality/valueThe proposed methods are simple to implement in large-scale parallel environment and can handle particle simulations with arbitrarily varying smoothing-lengths. The implemented smoothed-particle hydrodynamics solver has good parallel performance, suggesting the potential for other scientific applications.

Consistent SPH Simulations of Protostellar Collapse and Fragmentation

Abstract We study the consistency and convergence of smoothed particle hydrodynamics (SPH) as a function of the interpolation parameters, namely the number of particles N, the number of neighbors n, and the smoothing length h, using simulations of the collapse and fragmentation of protostellar rotating cores. The calculations are made using a modified version of the GADGET-2 code that employs an improved scheme for the artificial viscosity and power-law dependences of n and h on N, as was recently proposed by Zhu et al., which comply with the combined limit , , and with for full SPH consistency as the domain resolution is increased. We apply this realization to the “standard isothermal test case” in the variant calculated by Burkert & Bodenheimer and the Gaussian cloud model of Boss to investigate the response of the method to adaptive smoothing lengths in the presence of large density and pressure gradients. The degree of consistency is measured by tracking how well the estimates of the consistency integral relations reproduce their continuous counterparts. In particular, C 0 and C 1 particle consistency is demonstrated, meaning that the calculations are close to second-order accuracy. As long as n is increased with N, mass resolution also improves as the minimum resolvable mass . This aspect allows proper calculation of small-scale structures in the flow associated with the formation and instability of protostellar disks around the growing fragments, which are seen to develop a spiral structure and fragment into close binary/multiple systems as supported by recent observations.

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.

An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows

In this paper, an incompressible smoothed particle hydrodynamics (SPH) method is presented to solve unsteady free-surface flows. Both Newtonian and viscoelastic fluids are considered. In the case of viscoelastic fluids, both the Maxwell and Oldroyd-B models are investigated. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme and employs an adaptive smoothing length based on density variations. To alleviate the numerical difficulties encountered when fluid is highly stretched, an artificial stress term is incorporated into the momentum equation which reduces the risk of unrealistic fractures in the material. Two challenging test cases, the impacting drop and the jet buckling problems, are solved to demonstrate the capability of the proposed scheme in handling viscoelastic flows with complex free surfaces. The jet buckling test case was solved for a wide range of Weissenberg numbers. It was shown that in all cases the method is stable and fairly accurate and agrees well with the available data.

Adaptive smoothing lengths in SPH

Context: There is a need to improve the fidelity of SPH simulations of self-gravitating gas dynamics. Aims: We remind users of SPH that, if smoothing lengths are adjusted so as to keep the number of neighbours, ${\cal N}$, in the range ${\cal N}_{_{\rm NEIB}}\pm\Delta{\cal N}_{_{\rm NEIB}}$, the tolerance, $\Delta{\cal N}_{_{\rm NEIB}}$, should be set to zero, as first noted by Nelson & Papaloizou. We point out that this is a very straightforward and computationally inexpensive constraint to implement. Methods: We demonstrate this by simulating acoustic oscillations of a self-gravitating isentropic monatomic gas-sphere (cf. Lucy), using ${\cal N}_{_{\rm TOT}}\sim6,000$ particles and ${\cal N}_{_{\rm NEIB}}=50$. Results: We show that there is a marked reduction in the rates of numerical dissipation and diffusion as $\Delta{\cal N}_{_{\rm NEIB}}$ is reduced from 10 to zero. Moreover this reduction incurs a very small computational overhead. Conclusions: We propose that this should become a standard test for codes used in simulating star formation. It is a highly relevant test, because pressure waves generated by the switch from approximate isothermality to approximate adiabaticity play a critical role in the fragmentation of collapsing prestellar cores. Since many SPH simulations in the literature use ${\cal N}_{_{\rm NEIB}}=50$ and $\Delta{\cal N}_{_{\rm NEIB}}\geq10$, their results must be viewed with caution.

The cosmological simulation code gadget-2

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the `tree'-method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different timesteps. Individual and adaptive short-range timesteps may also be employed. The domain decomposition used in the parallelisation algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10^10 dark matter particles, reaching a homogeneous spatial dynamic range of 10^5 per dimension in a 3D box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community.

Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics

We present a new formulation of the equations of motion used in smoothed particle hydrodynamics (SPH). The spatial resolution in SPH is determined by the smoothing length, $h$, and it has become common practice for each particle to be given its own adaptive smoothing length, $h_i$. Consequently, the dynamic range that may be spatially resolved is greatly increased, but additional ($\nabla h$) terms, which account for the variability of the smoothing lengths, should appear in the equations of motion in order to satisy conservation requirements. Previous implementations of SPH have neglected these additional terms, whereas we have included them. This is achieved by defining a functional form for the $h_i$s, that depends on inter-particle distances only, and then deriving the equations of motion using a Hamiltonian formalism. A number of test calculations are presented. We find that including the $\nabla h$ terms has no detrimental effect on the ability of SPH to model known problems with reasonable accuracy. For problems where the energy conservation was rather poor, including the $\nabla h$ terms results in a dramatic improvement. In particluar non-conservation of energy during a collision between two polytropes can occur at the level of 10% when the $\nabla h$ terms are neglected. When the $\nabla h$ terms are included, then this error reduces to 0.8%.