Three-dimensional Smoothed Particle Hydrodynamics Simulations Research Articles

Direct imposition of the wall boundary condition for weakly compressible flows in three-dimensional smoothed particle hydrodynamics simulations

This study introduces a novel method for imposing wall boundary conditions in smoothed particle hydrodynamics (SPH). SPH is a particle method based on the Lagrangian approach, primarily employed in fluid analysis as a part of numerical computation methods. Due to its ability to discretize space using particles, SPH excels in handling analyses of free surface flow or multiphase flow with intricate boundary surfaces. However, there is a drawback in modeling wall boundaries using particles, as resolving the particle deficiency problem necessitates multi-layered boundary particles to be arranged behind the wall boundary. This leads to difficulties in implementing complex shapes and adds computational expense. To address this issue, this study suggests the use of boundary segments for wall boundary modeling and specifically employs triangular segments for three-dimensional expansions. For robust application of boundary conditions, a method considering both Poisson's equation and geometric configurations is proposed. The proposed method is independent of the segment density, which facilitates efficient and flexible modeling. In addition, by imposing accurate boundary conditions from the wall, the stability and accuracy of the solution are enhanced. The performance of the proposed method is validated through numerical examples, compared with various analytical and experimental results.

The role of the drag force in the gravitational stability of dusty planet-forming disc – II. Numerical simulations

ABSTRACT Young protostellar discs are likely to be both self-gravitating, and to support grain growth to sizes where the particles decoupled from the gas. This combination could lead to short-wavelength fragmentation of the solid component in otherwise non-fragmenting gas discs, forming Earth-mass solid cores during the Class 0/I stages of young stellar object evolution. We use three-dimensional smoothed particle hydrodynamics simulations of two-fluid discs, in the regime where the Stokes number of the particles St > 1, to study how the formation of solid clumps depends on the disc-to-star mass ratio, the strength of gravitational instability, and the Stokes number. Gravitational instability of the simulated discs is sustained by local cooling. We find that the ability of the spiral structures to concentrate solids increases with the cooling time and decreases with the Stokes number, while the relative dynamical temperature between gas and dust of the particles decreases with the cooling time and the disc-to-star mass ratio and increases with the Stokes number. Dust collapse occurs in a subset of high disc mass simulations, yielding clumps whose mass is close to linear theory estimates, namely 1–10 M⊕. Our results suggest that if planet formation occurs via this mechanism, the best conditions correspond to near the end of the self-gravitating phase, when the cooling time is long and the Stokes number close to unity.

Accretion rates in hierarchical triple systems with discs

ABSTRACT Young multiple systems accrete most of their final mass in the first few Myr of their lifetime, during the protostellar and protoplanetary phases. Previous studies showed that in binary systems the majority of the accreted mass falls on to the lighter star, thus evolving to mass equalization. However, young stellar systems often comprise more than two stars, which are expected to be in hierarchical configurations. Despite its astrophysical relevance, differential accretion in hierarchical systems remains to be understood. In this work, we investigate whether the accretion trends expected in binaries are valid for higher order multiples. We performed a set of three-dimensional smoothed particle hydrodynamics simulations of binaries and of hierarchical triples (HTs) embedded in an accretion disc, with the code phantom. We identify for the first time accretion trends in HTs and their deviations compared to binaries. These deviations, due to the interaction of the small binary with the infalling material from the circumtriple disc, can be described with a semi-analytical prescription. Generally, the smaller binary of an HT accretes more mass than a single star of the same mass as the smaller binary. We found that in an HT, if the small binary is heavier than the third body, the standard differential accretion scenario (whereby the secondary accretes more of the mass) is hampered. Reciprocally, if the small binary is lighter than the third body, the standard differential accretion scenario is enhanced. The peculiar differential accretion mechanism we find in HTs is expected to affect their mass ratio distribution.

Characteristics of iceberg calving-generated waves based on three-dimensional SPH simulations

Large-scale icebergs calving into water often generate waves that may threaten human lives or passing ships. The formation and evolution of such three-dimensional (3D) waves in the near field are still not fully understood. In this paper, a 3D numerical model based on the Smoothed Particle Hydrodynamics (SPH) open source code DualSPHysics was established to simulate the generation and evolution processes of waves caused by icebergs calving into water. The model is validated with available large-scale laboratory tests. The 3D characteristics in the near field of the waves are presented and analyzed in detail. The results indicate that iceberg calving can generate three main waves: a leading wave produced by the initial entry of the iceberg into the water; a second wave induced by the collapse of the water jet; and a third wave caused by the resurfacing of the iceberg. The reflux tail blocked by the reflux front may appear prior to the second wave, which can develop into a constantly changing wavefront, and then form a step-like flow structure in the near field by linking these two wavefronts. The shapes of the multiple wavefronts outlined by the leading wave and the trailing waves in the near field are closely related to the iceberg geometry. However, the wavefronts gradually develop into a semicircular shape in the far field irrespective of the iceberg geometry. These findings are helpful for hazard assessments of iceberg calving-generated waves. • A rigid body–fluid coupled SPH model is established to simulate three-dimensional iceberg calving-generated waves (ICGW). • The three-dimensional characteristics of ICGWs in the near field are presented. • ICGW consists of three main waves: a leading wave; a second wave by water jet; and a third wave by resurfacing. • The generation and evolution processes of the multiple wavefronts are outlined.

Hiding Signatures of Gravitational Instability in Protoplanetary Disks with Planets

Abstract We carry out three-dimensional smoothed particle hydrodynamics simulations to show that a migrating giant planet strongly suppresses the spiral structure in self-gravitating disks. We present mock Atacama Large Millimeter/submillimeter Array (ALMA) continuum observations that show that in the absence of a planet, spiral arms due to gravitational instability are easily observed. Whereas in the presence of a giant planet, the spiral structures are suppressed by the migrating planet resulting in a largely axisymmetric disk with a ring and gap structure. Our modeling of the gas kinematics shows that the planet’s presence could be inferred, for example, using optically thin 13C16O. Our results show that it is not necessary to limit the gas mass of disks by assuming high dust-to-gas mass ratios in order to explain a lack of spiral features that would otherwise be expected in high-mass disks.

Simulations of globular clusters within their parent galaxies: multiple stellar populations and internal kinematics

ABSTRACT Using three-dimensional smoothed particle hydrodynamics simulations, we investigate the formation of multiple stellar populations (MSPs) in globular clusters (GCs) within the context of their parent galaxies. In our scenario, the second generation (2G) of stars originate from both asymptotic giant branch (AGB) polluters and pristine gas accreted from the host galaxy. Previous theoretical and numerical studies have demonstrated that this ‘AGB with dilution’ model has the potential to alleviate several problems faced by the classical AGB scenario. However, the accretion of pristine gas on to the GC has yet to be investigated within the context of the parent galaxy. This paper presents the preliminary results from our original simulation code which models GC formation from giant molecular clouds in a host galaxy, and subsequent gas accretion on to the GC. By simulating the genesis of the 2G over a 370 Myr time frame, we demonstrate that the fraction of 2G stars are inextricably linked to the GC’s environment. Our simulations rationalize the wide variety of abundance patterns, kinematics, and 2G concentrations by altering the initial conditions of both the GC progenitor and the host galaxy itself. Most notably, we reproduce a positive correlation between the fraction of 2G stars and the initial mass of the cluster. We discuss the physical implications of our scenario and compare our simulations with observations of the Galactic GC 47 Tucanae (47 Tuc). Finally, we present scaling relations that encompass the wider GC population and serve as a reference for future observations.

Tidal Disruption Flares from Stars on Marginally Bound and Unbound Orbits

Abstract We study the mass fallback rate of tidally disrupted stars on marginally bound and unbound orbits around a supermassive black hole (SMBH) by performing three-dimensional smoothed particle hydrodynamic simulations with three key parameters. The star is modeled by a polytrope with two different indexes (n = 1.5 and 3). The stellar orbital properties are characterized by five orbital eccentricities ranging from e = 0.98 to 1.02, and five different penetration factors ranging from β = 1 to 3, where β represents the ratio of the tidal disruption to pericenter distance radii. We derive analytic formulae for the mass fallback rate as a function of the stellar density profile, orbital eccentricity, and penetration factor. Moreover, two critical eccentricities to classify tidal disruption events (TDEs) into five different types: eccentric ( ), marginally eccentric ( ), purely parabolic (e = 1), marginally hyperbolic ( ), and hyperbolic ( ) TDEs, are reevaluated as and , where q is the ratio of the SMBH to stellar masses and 0 < k ≲ 2. We find the asymptotic slope of the mass fallback rate varies with the TDE type. The asymptotic slope approaches −5/3 for the parabolic TDEs, is steeper for the marginally eccentric TDEs, and is flatter for the marginally hyperbolic TDEs. For the marginally eccentric TDEs, the peak of mass fallback rates can be about one order of magnitude larger than the parabolic TDE case. For marginally hyperbolic TDEs, the mass fallback rates can be much lower than the Eddington accretion rate, which can lead to the formation of a radiatively inefficient accretion flow, while hyperbolic TDEs lead to failed TDEs. Marginally unbound TDEs could be an origin of a very low-density gas disk around a dormant SMBH.

Planet migration in self-gravitating discs: survival of planets

ABSTRACT We carry out three-dimensional smoothed particle hydrodynamics simulations to study whether planets can survive in self-gravitating protoplanetary discs. The discs modelled here use a cooling prescription that mimics a real disc, which is only gravitationally unstable in the outer regions. We do this by modelling the cooling using a simplified method such that the cooling time in the outer parts of the disc is shorter than in the inner regions, as expected in real discs. We find that both giant (>MSat) and low-mass (<MNep) planets initially migrate inwards very rapidly, but are able to slow down in the inner gravitationally stable regions of the disc without needing to open up a gap. This is in contrast to previous studies where the cooling was modelled in a more simplified manner where, regardless of mass, the planets were unable to slow down their inward migration. This shows the important effect the thermodynamics has on planet migration. In a broader context, these results show that planets that form in the early stages of the discs’ evolution, when they are still quite massive and self-gravitating, can survive.

Experimental Validation of Single- and Two-Phase Smoothed Particle Hydrodynamics on Sloshing in a Prismatic Tank

This study aimed to validate the single-phase and two-phase smoothed particle hydrodynamics (SPH) on sloshing in a tank. There have been many studies on sloshing in tanks based on meshless particle methods, but few researchers have used a large number of particles because there is a limitation on the total number of particles when using only CPUs. Additionally, few studies have investigated the influence of air phase on tank sloshing based on two-phase SPH. In this study, a dedicated sloshing experiment was conducted at the National Research Institute of Fishing Engineering using a prismatic tank with a four-degrees-of-freedom forced oscillation machine. Three pressure gauges were used to measure local pressure near the corners of the tank. The sloshing experiment was repeated for two different filling ratios, amplitudes, and frequencies of external oscillation. Next, a GPU-accelerated three-dimensional SPH simulation of sloshing was performed using the same conditions as the experiment with a large number of particles. Lastly, two-dimensional sloshing simulations based on single-phase and two-phase SPH were carried out to determine the importance of the air phase in terms of tank sloshing. Based on systematic comparisons of the single-phase SPH, two-phase SPH, and experimental results, this paper presents a detailed discussion of the role of air-phase in terms of sloshing. The currently achievable accuracy when using SPH is demonstrated together with a few sensitivity analyses of SPH parameters.

SPH Simulations of the Induced Gravitational Collapse Scenario of Long Gamma-Ray Bursts Associated with Supernovae

Abstract We present the first three-dimensional smoothed particle hydrodynamics simulations of the induced gravitational collapse scenario of long-duration gamma-ray bursts (GRBs) associated with supernovae (SNe). We simulate the SN explosion of a carbon–oxygen core (COcore) forming a binary system with a neutron star (NS) companion. We follow the evolution of the SN ejecta, including their morphological structure, subject to the gravitational field of both the new NS (νNS) formed at the center of the SN and the one of the NS companion. We compute the accretion rate of the SN ejecta onto the NS companion, as well as onto the νNS from SN matter fallback. We determine the fate of the binary system for a wide parameter space including different COcore and NS companion masses, orbital periods, and SN explosion geometry and energies. We identify, for selected NS nuclear equations of state, the binary parameters leading the NS companion, by hypercritical accretion, either to the mass-shedding limit or to the secular axisymmetric instability for gravitational collapse to a black hole (BH), or to a more massive, fast-rotating, stable NS. We also assess whether the binary remains gravitationally bound after the SN explosion, hence exploring the space of binary and SN explosion parameters leading to νNS–NS and νNS–BH binaries. The consequences of our results for the modeling of long GRBs, i.e., X-ray flashes and binary-driven hypernovae, are discussed.

Three-dimensional smoothed particle hydrodynamics simulation for injection molding flow of short fiber-reinforced polymer composites

This paper investigates the three-dimensional (3D) injection molding flow of short fiber-reinforced polymer composites using a smoothed particle hydrodynamics (SPH) simulation method. The polymer melt was modeled as a power law fluid and the fibers were considered as rigid cylindrical bodies. The filling details and fiber orientation in the injection-molding process were studied. The results indicated that the SPH method could effectively predict the order of filling, fiber accumulation, and heterogeneous distribution of fibers. The SPH simulation also showed that fibers were mainly aligned to the flow direction in the skin layer and inclined to the flow direction in the core layer. Additionally, the fiber-orientation state in the simulation was quantitatively analyzed and found to be consistent with the results calculated by conventional tensor methods.

On the Origin of the Spiral Morphology in the Elias 2–27 Circumstellar Disk

Abstract The young star Elias 2–27 has recently been observed to posses a massive circumstellar disk with two prominent large-scale spiral arms. In this Letter, we perform three-dimensional Smoothed Particle Hydrodynamics simulations, radiative transfer modeling, synthetic ALMA imaging, and an unsharped masking technique to explore three possibilities for the origin of the observed structures—an undetected companion either internal or external to the spirals, and a self-gravitating disk. We find that a gravitationally unstable disk and a disk with an external companion can produce morphology that is consistent with the observations. In addition, for the latter, we find that the companion could be a relatively massive planetary-mass companion (≲10–13 M Jup) and located at large radial distances (between ≈300–700 au). We therefore suggest that Elias 2–27 may be one of the first detections of a disk undergoing gravitational instabilities, or a disk that has recently undergone fragmentation to produce a massive companion.

Theory and simulation of the dynamics, deformation, and breakup of a chain of superparamagnetic beads under a rotating magnetic field

In this work, an analytical model for the behavior of superparamagnetic chains under the effect of a rotating magnetic field is presented. It is postulated that the relevant mechanisms for describing the shape and breakup of the chains into smaller fragments are the induced dipole-dipole magnetic force on the external beads, their translational and rotational drag forces, and the tangential lubrication between particles. Under this assumption, the characteristic S-shape of the chain can be qualitatively understood. Furthermore, based on a straight chain approximation, a novel analytical expression for the critical frequency for the chain breakup is obtained. In order to validate the model, the analytical expressions are compared with full three-dimensional smoothed particle hydrodynamics simulations of magnetic beads showing excellent agreement. Comparison with previous theoretical results and experimental data is also reported.

Circularization of tidally disrupted stars around spinning supermassive black holes

We study the circularization of tidally disrupted stars on bound orbits around spinning supermassive black holes by performing three-dimensional smoothed particle hydrodynamic simulations with Post-Newtonian corrections. Our simulations reveal that debris circularization depends sensitively on the efficiency of radiative cooling. There are two stages in debris circularization if radiative cooling is inefficient: first, the stellar debris streams self-intersect due to relativistic apsidal precession; shocks at the intersection points thermalize orbital energy and the debris forms a geometrically thick, ring-like structure around the black hole. The ring rapidly spreads via viscous diffusion, leading to the formation of a geometrically thick accretion disk. In contrast, if radiative cooling is efficient, the stellar debris circularizes due to self-intersection shocks and forms a geometrically thin ring-like structure. In this case, the dissipated energy can be emitted during debris circularization as a precursor to the subsequent tidal disruption flare. The possible radiated energy is up to ~2*10^{52} erg for a 1 Msun star orbiting a 10^6 Msun black hole. We also find that a retrograde (prograde) black hole spin causes the shock-induced circularization timescale to be shorter (longer) than that of a non-spinning black hole in both cooling cases. The circularization timescale is remarkably long in the radiatively efficient cooling case, and is also sensitive to black hole spin. Specifically, Lense-Thirring torques cause dynamically important nodal precession, which significantly delays debris circularization. On the other hand, nodal precession is too slow to produce observable signatures in the radiatively inefficient case. We also discuss the relationship between our simulations and the parabolic TDEs that are characteristic of most stellar tidal disruptions.

Angular momentum distribution during the collapse of primordial star-forming clouds

It is generally believed that angular momentum is distributed during the gravitational collapse of the primordial star forming cloud. However, so far there has been little understanding of the exact details of the distribution. We use the modified version of the Gadget-2 code, a three-dimensional smoothed-particle hydrodynamics simulation, to follow the evolution of the collapsing gas in both idealized as well as more realistic minihalos. We find that, despite the lack of any initial turbulence and magnetic fields in the clouds the angular momentum profile follows the same characteristic power-law that has been reported in studies that employed fully self-consistent cosmological initial conditions. The fit of the power-law appears to be roughly constant regardless of the initial rotation of the cloud. We conclude that the specific angular momentum of the self-gravitating rotating gas in the primordial minihalos maintains a scaling relation with the gas mass as $L \propto M^{1.125}$. We also discuss the plausible mechanisms for the power-law distribution.

Apsidal precession, disc breaking and viscosity in warped discs

Abstract We demonstrate the importance of general relativistic apsidal precession in warped black hole accretion discs by comparing three-dimensional smoothed particle hydrodynamic simulations in which this effect is first neglected, and then included. If apsidal precession is neglected, we confirm the results of an earlier magnetohydrodynamic simulation which made this assumption, showing that at least in this case the α viscosity model produces very similar results to those of simulations where angular momentum transport is due to the magnetorotational instability. Including apsidal precession significantly changes the predicted disc evolution. For moderately inclined discs thick enough that tilt is transported by bending waves, we find a disc tilt which is non-zero at the inner disc edge and oscillates with radius, consistent with published analytic results. For larger inclinations, we find disc breaking.

SIMULATED IMPACTS TO NON-MAGNETIC CATACLYSMIC VARIABLE DISKS

Dust has recently been found to be prevalent in compact binaries such as non-magnetic Cataclysmic Variable systems. As a possible source of this dust is from solid bodies, we explore impacts to non-magnetic Cataclysmic Variable disks. We use three-dimensional Smoothed Particle Hydrodynamic simulations to search for impact signatures. From injections of whole bodies to these disks, we nd pulse shapes in simulated bolometric light curves that resemble impact ashes in the light curves of the Shoemaker-Levy 9 event. As a result, we tentatively identify these light curve shapes as signatures of impacts.

DNS and LES of 3-D wall-bounded turbulence using Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics (SPH) has been used in the simulation of fluid flows for several years. Recently, SPH saw its range of applications extended to the simulation of real-world engineering applications which often concern the simulation of turbulent three-dimensional flows. However, there is a significant lack in the investigation of such turbulent flows even for simplified applications. Most three-dimensional SPH simulations that analyze properties of a turbulent flow examine the decay of isotropic turbulence, where no solid walls influence the flow. In the present paper several three-dimensional turbulent channel flows are simulated using the SPH method to address this gap in literature. The first set of simulations investigates a quasi direct numerical simulation (DNS) of a channel with reduced size. This enables evaluation of SPH as a pure Navier–Stokes solver by avoiding the introduction of turbulence models. The results show the correct reproduction of the turbulent statistics except for some fluctuations in the near wall region. The second set of simulations attempts a large eddy simulation (LES) of a standard size channel. It is shown that the present SPH formulation fails to reproduce the correct turbulent statistics and the cause for this failure is analyzed with the aide of the Taylor–Green vortex flow and attributed to incorrect reproduction of velocity–pressure interactions by the collocated and large stencil SPH discretisation.

Growth and fragmentation of centimetre-sized dust aggregates: the dependence on aggregate size and porosity

We carry out three-dimensional Smoothed Particle Hydrodynamics simulations of spherical homogeneous SiO2 dust aggregates to investigate how the mass and the porosity of the aggregates affects their ability to survive an impact at various different collision velocities (between 1 - 27.5m/s). We explore how the threshold velocities for fragmentation vary with these parameters. Crucially, we find that the porosity plays a part of utmost importance in determining the outcome of collisions. In particular, we find that aggregates with filling factors >37% are significantly weakened and that the velocity regime in which the aggregates grow is reduced or even non-existent (instead, the aggregates either rebound off each other or break apart). At filling factors less than ~37% we find that more porous objects are weaker but not as weak as highly compact objects with filling factors >37%. In addition we find that (for a given aggregate density) collisions between very different mass objects have higher threshold velocities than those between very similar mass objects. We find that fragmentation velocities are higher than the typical values of 1m/s and that growth can even occur for velocities as high as 27.5m/s. Therefore, while the growth of aggregates is more likely if collisions between different sized objects occurs or if the aggregates are porous with filling factor <37%, it may also be hindered if the aggregates become too compact.

Binary Black Hole Accretion Flows From a Misaligned Circumbinary Disk

We studied the basic properties of accretion flows onto binary supermassive black holes, including cases in which a circumbinary disk is misaligned with the binary orbital plane, by means of three-dimensional smoothed particle hydrodynamics simulations. We find that a circular binary system with a misaligned circumbinary disk normally produces a double-peaked mass-accretion-rate variation per binary orbit. This is because each black hole passes across the circumbinary disk plane and captures gas twice in one orbital period. Even in misaligned systems, however, a single peaked mass-accretion-rate variation per binary orbit is produced, if the orbital eccentricity is moderately large ($e \gtrsim$ 0.3). The number of peaks in the mass accretion rates can be understood simply in terms of the orbital phase dependence of the distance between each binary black hole and its closest inner edge of the circumbinary disk. In the cases of eccentric binary black holes having different masses, the less massive black hole can get closer to the circumbinary disk than the massive one, thus tidally splitting gas from its inner edge, but the created gas flows are comparably captured by both black holes with a short time delay. As a consequence, the combined light curve shows periodic occurrence of double-peaked flares with a short interval. This may account for the observed light variations of OJ287.