Smoothed Particle Hydrodynamics Calculations Research Articles

Study on the effect of cavity oscillation on wedge water entry with a multiphase smoothed particle hydrodynamics model

Previous Smoothed Particle Hydrodynamics (SPH) study on water entry issues has primarily been conducted for the load analysis of impact phase rather than the cavity oscillation effect because the calculation and simulation of this complex physical process are more complicated and time consuming. In order to increase computational efficiency and accuracy, the multiphase δ+-SPH model is combined with Adaptive Particle Refinement technology to investigate the whole process of the wedge's water entry. The hydrodynamic phenomena in the stages before cavity closure for the four cases with different Froude numbers (Fn) are compared and analyzed. After the cavity is pinched off, the wedge exhibits kinematic oscillation. Our test shows that the adoption of sound speed has a significant influence on the oscillation period and peak value of closed cavities in weakly compressible SPH calculations. Then, a suitable sound speed adoption is selected to simulate the oscillatory phenomenon accurately. Comparing the pressure profile with the surface pressure and acceleration of the wedge at the same time, it can be concluded that the oscillation of the hydrodynamic load on the wedge is caused by the pressure oscillation in the closed cavity. Especially for the case of low Fn, the pressure peak on the wedge's surface in the oscillation stage is even greater than the pressure load in the impact stage. The peak pressure of closed cavity is positively correlated with Fn and negatively correlated with Euler number (Eu). Finally, by analyzing the influence of wedge width and impact velocity, it is found that the oscillation period of the closed cavity is related to the morphology of the cavity. The larger the aspect ratio of the closed cavity, the longer the oscillation period.

Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process

This paper presents an efficient mesoscale simulation of a Laser Powder Bed Fusion (LPBF) process using the Smoothed Particle Hydrodynamics (SPH) method. The efficiency lies in reducing the computational effort via spatial adaptivity, for which a dynamic particle refinement pattern with an optimized neighbor-search algorithm is used. The melt pool dynamics is modeled by resolving the thermal, mechanical, and material fields in a single laser track application. After validating the solver by two benchmark tests where analytical and experimental data are available, we simulate a single-track LPBF process by adopting SPH in multi resolutions. The LPBF simulation results show that the proposed adaptive refinement with and without an optimized neighbor-search approach saves almost 50% and 35% of the SPH calculation time, respectively. This achievement enables several opportunities for parametric studies and running high-resolution models with less computational effort.

Smoothed Particle Hydrodynamics Modeling of Natural Convection Around a Heated Horizontal Cylinder: A Comparison With Experiments

AbstractAn experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers (1.18≤Ra≤242). Both the experiments and the SPH calculations were performed for positive (0.1≤ΔT≤10 K) and negative (−10≤ΔT≤−0.1 K) temperature differences between the source and the surrounding fluid. In all cases, a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for ΔT>0 and a vertically descending flow just below the source for ΔT<0. The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors (RMSE) in the velocity profiles of the order of ∼10−5 m s−1. The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach.

A novel approach to determine residual stress field during FSW of AZ91 Mg alloy using combined smoothed particle hydrodynamics/neuro-fuzzy computations and ultrasonic testing

The faults in welding design and process every so often yield defective parts during friction stir welding (FSW). The development of numerical approaches including the finite element method (FEM) provides a way to draw a process paradigm before any physical implementation. It is not practical to simulate all possible designs to identify the optimal FSW practice due to the inefficiency associated with concurrent modeling of material flow and heat dissipation throughout the FSW. This study intends to develop a computational workflow based on the mesh-free FEM framework named smoothed particle hydrodynamics (SPH) which was integrated with adaptive neuro-fuzzy inference system (ANFIS) to evaluate the residual stress in the FSW process. An integrated SPH and ANFIS methodology was established and the well-trained ANIS was then used to predict how the FSW process depends on its parameters. To verify the SPH calculation, an itemized FSW case was performed on AZ91 Mg alloy and the induced residual stress was measured by ultrasonic testing. The suggested methodology can efficiently predict the residual stress distribution throughout friction stir welding of AZ91 alloy.

Efficiency of particle search methods in smoothed particle hydrodynamics: a comparative study (part I)

Nearest neighbour searching is central to the efficiency of smoothed particle hydrodynamics (SPH). Here the performance of the brute force (BF) or direct search (DS), the cell-linked list (CLL), and the KD-tree (KDT) methods in vectorised form are analysed. The results indicate that the efficiency of the SPH calculations is improved with the vectorised cell-linked list (VCLL) and the vectorised KD-tree (VKDT). However, the VKDT approach is more efficient than the VCLL method for N ≤ 105 in two dimensions (2D) and N ≤ 106 in three dimensions (3D). For larger N, the time duration of the SPH calculations with the VKDT method grows steeply while a linear trend is maintained with the VCLL. The complexity here is measured not only for early events but also close to the point of hardware limit, in which the complexity has a different behaviour, which can be measured and compared using a power fit.

An incompressible–compressible Lagrangian particle method for bubble flows with a sharp density jump and boiling phase change

Modeling the boiling phase change is particularly challenging for Lagrangian particle methods due to a high density ratio and dramatic volume expansion. In this study, the incompressible moving particle semi-implicit (MPS) method and the weakly compressible smoothed particle hydrodynamics (SPH) method are coupled to develop an incompressible–compressible particle method for modeling a multiphase flow with boiling. The coupling strategies developed by Lind et al. (JCP, 2016) are adopted. A high speed of sound must be employed in SPH for incompressible bubbles in a heavy liquid under gravity, which can cause severe spurious pressure fluctuations. In this situation, a technique for detecting bubble connectivity is developed to average the pressure inside each bubble for stable coupling. This pressure averaging strategy is physically consistent due to the high density ratio. Because the pressure coupling strategy tends to break the force balance between the surface tension and the pressure jump across the interface, the surface tension model must be based only on the liquid particles near the interface. The boiling mass transfer is modeled in a straightforward manner by injecting gas particles towards the gas phase from the liquid interface particles. The gas volume expansion is naturally considered by the coupling method, as the gas particle distribution can be automatically regulated in the SPH calculation. Rising bubble simulations with different surface tension coefficients and density ratios verify the proposed method for a bubble flow. The Stefan and sucking problems as well as a horizontal film boiling flow are simulated to verify the boiling model and to demonstrate its straightforward capability to handle gas volume expansion.

An Improved Support Domain Model of Smoothed Particle Hydrodynamics Method to Simulate Crack Propagation in Materials

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension, which improves the support domains of crack tip particles. Based on the principle of minimum strain energy density factor in fracture mechanics, the initiation and extended directions of cracks in materials are estimated. By simulating the generation and expansion of three modes of cracks in materials, the SPH calculation results of the three types of support domain forms are compared with the ABAQUS simulation results and experiment results. It indicates that the method of virtual crack boundary method is more stable than the one based on discontinuous medium. And it can generate more reasonable results than the method based on continuous medium. This paper proves the effectiveness of strain energy density factor based on fracture mechanics theory in searching the direction of crack expansion using SPH, and explores the application of new support domain model in SPH crack solution.

The Kelvin–Helmholtz instability and smoothed particle hydrodynamics

ABSTRACT We perform simulations of the Kelvin–Helmholtz instability using smoothed particle hydrodynamics (SPH). The instability is studied both in the linear and strongly non-linear regimes. The smooth, well-posed initial conditions of Lecoanet et al. (2016) are used, along with an explicit Navier–Stokes viscosity and thermal conductivity to enforce the evolution in the non-linear regime. We demonstrate convergence to the reference solution using SPH. The evolution of the vortex structures and the degree of mixing, as measured by a passive scalar ‘colour’ field, match the reference solution. Tests with an initial density contrast produce the correct qualitative behaviour. The $\mathcal {L}_2$ error of the SPH calculations decreases as the resolution is increased. The primary source of error is numerical dissipation arising from artificial viscosity, and tests with reduced artificial viscosity have reduced $\mathcal {L}_2$ error. A high-order smoothing kernel is needed in order to resolve the initial velocity amplitude of the seeded mode and inhibit excitation of spurious modes. We find that standard SPH with an artificial viscosity has no difficulty in correctly modelling the Kelvin–Helmholtz instability and yields convergent solutions.

Impetus: consistent SPH calculations of 3D spherical Bondi accretion on to a black hole

We present three-dimensional calculations of spherically symmetric Bondi accretion onto a stationary supermassive black hole (SMBH) of mass $10^{8}$ $M_{\odot}$ within a radial range of $0.02-10$ pc, using a modified version of the smoothed particle hydrodynamics (SPH) \gad \sp code, which ensures approximate first-order consistency (i.e., second-order accuracy) for the particle approximation. First-order consistency is restored by allowing the number of neighbours, $n_{\rm neigh}$, and the smoothing length, $h$, to vary with the total number of particles, $N$, such that the asymptotic limits $n_{\rm neigh}\to\infty$ and $h\to 0$ hold as $N\to\infty$. The ability of the method to reproduce the isothermal ($\gamma =1$) and adiabatic ($\gamma =5/3$) Bondi accretion is investigated with increased spatial resolution. In particular, for the isothermal models the numerical radial profiles closely match the Bondi solution, except near the accretor, where the density and radial velocity are slightly underestimated. However, as $n_{\rm neigh}$ is increased and $h$ is decreased, the calculations approach first-order consistency and the deviations from the Bondi solution decrease. The density and radial velocity profiles for the adiabatic models are qualitatively similar to those for the isothermal Bondi accretion. Steady-state Bondi accretion is reproduced by the highly resolved consistent models with a percent relative error of $\lesssim 1$\% for $\gamma =1$ and $\sim 9$\% for $\gamma =5/3$, with the adiabatic accretion taking longer than the isothermal case to reach steady flow. The performance of the method is assessed by comparing the results with those obtained using the standard Gadget and the Gizmo codes.

Two-dimensional free-surface flow under gravity: A new benchmark case for SPH method

Currently there are few free-surface benchmark cases with analytical results for the Smoothed Particle Hydrodynamics (SPH) simulation. In the present contribution we introduce a two-dimensional free-surface flow under gravity, and obtain an analytical expression on the surface height difference and a theoretical estimation on the surface fractal dimension. They are preliminarily validated and supported by SPH calculations.

On the origin of horseshoes in transitional discs

We investigate whether the rings, lopsided features and horseshoes observed at millimetre wavelengths in transitional discs can be explained by the dynamics of gas and dust at the edge of the cavity in circumbinary discs. We use 3D dusty smoothed particle hydrodynamics calculations to show that binaries with mass ratio $q \gtrsim 0.04$ drive eccentricity in the central cavity, naturally leading to a crescent-like feature in the gas density, which is accentuated in the mm dust grain population with intensity contrasts in mm-continuum emission of 10 or higher. We perform mock observations to demonstrate that these features closely match those observed by ALMA, suggesting that the origin of rings, dust horseshoes and other non-axisymmetric structures in transition discs can be explained by the presence of massive companions.

Cool and luminous transients from mass-losing binary stars

Motivated by the recently established link between luminous red novae (LRN) and catastrophic phases of binary star evolution, we perform smoothed particle hydrodynamic calculations of outflows from binary stars with realistic equation of state and opacities. We focus on the case of mass loss from the outer Lagrangian point (L2), where the resulting spiral stream experiences tidal torques from the binary and becomes unbound. As the individual spiral arms merge and collide near the binary, the outflow thermalizes about 5% of its kinetic energy. For reasonable binary parameters, the outflow can produce luminosities up to 106 L⨀ with effective temperatures between 500 and 6000 K, depending on the optical depth through the outflow. This is compatible with many examples of the LRN such as V838 Mon and V1309 Sco. The luminosity and the expansion velocity are correlated, as is roughly observed in the known LRN. The outflow readily forms dust, leading to great variations of the appearance of the transient as a function of the viewing angle. Our results are relevant for a more general class of equatorial outflows with asymptotic velocity and heating rate near the binary proportional to its orbital speed.

On planet formation in HL Tau

Abstract We explain the axisymmetric gaps seen in recent long-baseline observations of the HL Tau protoplanetary disc with the Atacama Large Millimetre/Submillimetre Array (ALMA) as being due to the different response of gas and dust to embedded planets in protoplanetary discs. We perform global, three-dimensional dusty smoothed particle hydrodynamics calculations of multiple planets embedded in dust/gas discs which successfully reproduce most of the structures seen in the ALMA image. We find a best match to the observations using three embedded planets with masses of 0.2, 0.27 and 0.55 MJ in the three main gaps observed by ALMA, though there remain uncertainties in the exact planet masses from the disc model.

Mesoscale Study of Proton Transport in Proton Exchange Membranes: Role of Morphology

The influence of morphology on proton transport in proton exchange membranes (PEM) is studied at the mesoscale using smoothed particle hydrodynamics (SPH), a mesh-free particle method for solving continuity equations. By solving the Nernst–Planck equation for proton transport in lamellar, cylinder, and cluster morphologies, we find that the proton conductivity for cluster morphology is much lower than lamellar and cylinder morphology at all hydration levels. This suggests the porosity and tortuosity in PEM morphology can reduce proton transport significantly at the mesoscale. We also investigated the effect of including a position-dependent diffusion constant (PDDC) tied to the local morphology, which is usually ignored in studies of proton transport in confinement. We calculated the PDDC in lamellar PEM using both quantitative and phenomenological approaches. SPH calculations show that conductivities for PEM systems with a PDDC can vary compared with systems with uniform diffusion constant. Therefore, it is potentially important to take into account the inhomogeneity of transport coefficients when studying proton transport in anisotropic systems.

Equalizing resolution in smoothed-particle hydrodynamics calculations using self-adaptive sinc kernels

The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy, with a resolution that is usually much higher in the compressed regions than in the diluted zones of the fluid. In this work, we propose and check a scheme to balance and equalize the resolution of SPH between high- and low-density regions. This method relies on the versatility of a family of interpolators called Sinc kernels, which allows increasing the interpolation quality by varying only a single parameter (the exponent of the Sinc function). The scheme is checked and validated through a number of numerical tests, from standard one-dimensional Riemann problems in shock tubes, to multidimensional simulations of explosions, hydrodynamic instabilities and the collapse of a sun-like polytrope. The analysis of the hydrodynamical simulations suggests that the scheme devised to equalizing accuracy improves the treatment of the post-shock regions and, in general, of the rarefacted zones of fluids while causing no harm to the growth of hydrodynamic instabilities. The method is robust and easy to implement with a low computational overload. It conserves mass, energy, and momentum and reduces to the standard SPH scheme in regions of the fluid that have smooth density gradients.

Investigation of the initial state of the Moon-forming disk: Bridging SPH simulations and hydrostatic models

According to the standard giant impact hypothesis, the Moon formed from a partially vaporized disk generated by a collision between the proto-Earth and a Mars-sized impactor. The initial structure of the disk significantly affects the Moon-forming process, including the Moon’s mass, its accretion time scale, and its isotopic similarity to Earth. The dynamics of the impact event determines the initial structure of a nearly hydrostatic Moon-forming disk. However, the hydrostatic and hydrodynamic models have been studied separately and their connection has not previously been well quantified. Here, we show the extent to which the properties of the disk can be inferred from Smoothed Particle Hydrodynamic (SPH) simulations. By using entropy, angular momentum and mass distributions of the SPH outputs as approximately conserved quantities, we compute the two-dimensional disk structure. We investigate four different models: (a) standard, the canonical giant impact model, (b) fast-spinning Earth, a collision between a fast-spinning Earth and a small impactor, (c) sub-Earths, a collision between two objects with half Earth’s mass, and (d) intermediate, a collision of two bodies whose mass ratio is 7:3. Our SPH calculations show that the initial disk has approximately uniform entropy. This is because the materials of different angular momenta are shocked to similar extents. The disks of the fast-spinning Earth and sub-Earths cases are hotter and more vaporized (∼80–90% vapor) than the standard case (∼20%). The intermediate case falls between these values. In the highly vaporized cases, our procedure fails to establish a unique surface density profile of the disk because the disk is unstable according to the Rayleigh criterion (the need for a monotonically increasing specific angular momentum with radius). In these cases, we estimate non-unique disk models by conserving global quantities (mass and total angular momentum). We also develop a semi-analytic model for the thermal structure of the disk, including the radial temperature structure and the vapor mass fraction. The model requires only two inputs: the average entropy and the surface density of the disk.

Radial migration in a bar-dominated disc galaxy – I. Impact on chemical evolution

We study radial migration and chemical evolution in a bar-dominated disc galaxy, by analysing the results of a fully self-consistent, high-resolution N-body+smoothed particle hydrodynamics (SPH) simulation. We find different behaviours for gas and star particles. Gas within corotation is driven in the central regions by the bar, where it forms a pseudo-bulge (discy-bulge), but it undergoes negligible radial displacement outside the bar region. Stars undergo substantial radial migration at all times, caused first by transient spiral arms and later by the bar. Despite the important amount of radial migration occurring in our model, its impact on the chemical properties is limited. The reason is the relatively flat abundance profile, due to the rapid early evolution of the whole disc. We show that the implications of radial migration on chemical evolution can be studied to a good accuracy by post-processing the results of the N-body+SPH calculation with a simple chemical evolution model having detailed chemistry and a parametrized description of radial migration. We find that radial migration impacts on chemical evolution both directly (by moving around the long-lived agents of nucleosynthesis, like e.g. SNIa or asymptotic giant branch stars, and thus altering the abundance profiles of the gas) and indirectly (by moving around the long-lived tracers of chemical evolution and thus affecting stellar metallicity profiles, local age-metallicity relations and metallicity distributions of stars, etc.).

Moving-mesh cosmology: properties of gas discs

We compare the structural properties of galaxies formed in cosmological simulations using the smoothed particle hydrodynamics (SPH) code GADGET with those using the moving-mesh code AREPO. Both codes employ identical gravity solvers and the same sub-resolution physics but use very different methods to track the hydrodynamic evolution of gas. This permits us to isolate the effects of the hydro solver on the formation and evolution of galactic gas disks in GADGET and AREPO haloes with comparable numerical resolution. In a matching sample of GADGET and AREPO haloes we fit simulated gas disks with exponential profiles. We find that the cold gas disks formed using the moving mesh approach have systematically larger disk scale lengths and higher specific angular momenta than their GADGET counterparts across a wide range in halo masses. For low mass galaxies differences between the properties of the simulated galaxy disks are caused by an insufficient number of resolution elements which lead to the artificial angular momentum transfer in our SPH calculation. We however find that galactic disks formed in massive halos, resolved with 10^6 particles/cells, are still systematically smaller in the GADGET run by a factor of ~2. The reasons for this are: 1) The excessive heating of haloes close to the cooling radius due to spurious dissipation of the subsonic turbulence in GADGET; and 2) The efficient delivery of low angular momentum gaseous blobs to the bottom of the potential well. While this large population of gaseous blobs in GADGET originates from the filaments which are pressure confined and fragment due to the SPH surface tension while infalling into hot halo atmospheres, it is essentially absent in the moving mesh calculation, clearly indicating numerical rather than physical origin of the blob material.

Modelling of equal channel angular pressing using a mesh-free method

Severe plastic deformation (SPD) processes are widely recognised as efficient techniques to produce bulk ultrafine-grained materials. As a complement to experiments, computational modelling is extensively used to understand the deformation mechanisms of grain refinement induced by large strain loading conditions. Although considerable research has been undertaken in the modelling of SPD processes, most of the studies have been accomplished using mesh-based methods, such as the finite element method (FEM). Mesh-based methods have inherent difficulties in modelling high-deformation processes because of the distortions in the mesh and the resultant inaccuracies and instabilities. As an alternative, a mesh-free method called smoothed particle hydrodynamics (SPH) is used. The effectiveness of this technique is highlighted for modelling of one of the most popular SPD techniques, equal channel angular pressing. A benchmark between SPH and FE calculation is performed. Furthermore, a number of simulations under different processing conditions are compared to existing literature data. A satisfactory agreement is found, which indicates that SPD processes can be approached by mesh-free methods, such as SPH.

On the onset of runaway stellar collisions in dense star clusters - II. Hydrodynamics of three-body interactions

The onset of runaway stellar collisions in young star clusters is more likely to initiate with an encounter between a binary and a third star than between two single stars. Using the initial conditions of such three-star encounters from direct N-body simulations, we model the resulting interaction by means of Smoothed Particle Hydrodynamics (SPH). Our code implements new equations of motion that allow for ecient use of non-equal mass particles and is capable of evolving contact binaries for thousands of orbits. We nd that, in the majority of the cases considered, all three stars merge together. In addition, we compare our SPH calculations against those of the sticky-sphere approximation. If one is not concerned with mass loss, then the sticky sphere approach gives the correct qualitative outcome in approximately 75% of the cases considered. Among those cases in which the sticky-sphere algorithm identies only two particular stars to collide, the hydrodynamic calculations nd the same