Smoothed Particle Hydrodynamics Code Research Articles

Moving-mesh cosmology: characteristics of galaxies and haloes

We discuss cosmological hydrodynamic simulations of galaxy formation performed with the new moving-mesh code arepo, which promises higher accuracy compared with the traditional smoothed particle hydrodynamics (SPH) technique that has been widely employed for this problem. In this exploratory study, we deliberately limit the complexity of the physical processes followed by the code for ease of comparison with previous calculations, and include only cooling of gas with a primordial composition, heating by a spatially uniform ultraviolet background, and a simple subresolution model for regulating star formation in the dense interstellar medium. We use an identical set of physics in corresponding simulations carried out with the well-tested SPH code gadget, adopting also the same high-resolution gravity solver. We are thus able to compare both simulation sets on an object-by-object basis, allowing us to cleanly isolate the impact of different hydrodynamical methods on galaxy and halo properties. In accompanying papers, Vogelsberger et al. and Sijacki et al., we focus on an analysis of the global baryonic statistics predicted by the simulation codes, and complementary idealized simulations that highlight the differences between the hydrodynamical schemes. Here we investigate their influence on the baryonic properties of simulated galaxies and their surrounding haloes. We find that arepo leads to significantly higher star formation rates for galaxies in massive haloes and to more extended gaseous discs in galaxies, which also feature a thinner and smoother morphology than their gadget counterparts. Consequently, galaxies formed in arepo have larger sizes and higher specific angular momentum than their SPH correspondents. Interestingly, the more efficient cooling flows in arepo yield higher densities and lower entropies in halo centres compared to gadget, whereas the opposite trend is found in halo outskirts. The cooling differences leading to higher star formation rates of massive galaxies in arepo also slightly increase the baryon content within the virial radius of massive haloes. We show that these differences persist as a function of numerical resolution. While both codes agree to acceptable accuracy on a number of baryonic properties of cosmic structures, our results thus clearly demonstrate that galaxy formation simulations greatly benefit from the use of more accurate hydrodynamical techniques such as arepo and call into question the reliability of galaxy formation studies in a cosmological context using traditional standard formulations of SPH, such as the one implemented in gadget. Our new moving-mesh simulations demonstrate that a population of extended gaseous discs of galaxies in large volume cosmological simulations can be formed even without energetic feedback in the form of galactic winds, although such outflows appear required to obtain realistic stellar masses.

Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters

Starting from the single graphics processing unit (GPU) version of the Smoothed Particle Hydrodynamics (SPH) code DualSPHysics, a multi-GPU SPH program is developed for free-surface flows. The approach is based on a spatial decomposition technique, whereby different portions (sub-domains) of the physical system under study are assigned to different GPUs. Communication between devices is achieved with the use of Message Passing Interface (MPI) application programming interface (API) routines. The use of the sorting algorithm radix sort for inter-GPU particle migration and sub-domain “halo” building (which enables interaction between SPH particles of different sub-domains) is described in detail. With the resulting scheme it is possible, on the one hand, to carry out simulations that could also be performed on a single GPU, but they can now be performed even faster than on one of these devices alone. On the other hand, accelerated simulations can be performed with up to 32 million particles on the current architecture, which is beyond the limitations of a single GPU due to memory constraints. A study of weak and strong scaling behaviour, speedups and efficiency of the resulting program is presented including an investigation to elucidate the computational bottlenecks. Last, possibilities for reduction of the effects of overhead on computational efficiency in future versions of our scheme are discussed.

Magicc haloes: confronting simulations with observations of the circumgalactic medium at z=0

We explore the circumgalactic medium (CGM) of two simulated star-forming galaxies with luminosities L ~ 0.1 and 1 L* generated using the smooth particle hydrodynamic code GASOLINE. These simulations are part of the Making Galaxies In a Cosmological Context (MAGICC) program in which the stellar feedback is tuned to match the stellar mass-halo mass relationship. For comparison, each galaxy was also simulated using a 'lower feedback' (LF) model which has strength comparable to other implementations in the literature. The 'MAGICC feedback' (MF) model has a higher incidence of massive stars and an approximately two times higher energy input per supernova. Apart from the low-mass halo using LF, each galaxy exhibits a metal-enriched CGM that extends to approximately the virial radius. A significant fraction of this gas has been heated in supernova explosions in the disc and subsequently ejected into the CGM where it is predicted to give rise to substantial O VI absorption. The simulations do not yet address the question of what happens to the O VI when the galaxies stop forming stars. Our models also predict a reservoir of cool H I clouds that show strong Ly\alpha absorption to several hundred kpc. Comparing these models to recent surveys with the Hubble Space Telescope, we find that only the MF models have sufficient O VI and H I gas in the CGM to reproduce the observed distributions. In separate analyses, these same MF models also show better agreement with other galaxy observables (e.g. rotation curves, surface brightness profiles and H I gas distribution). We infer that the CGM is the dominant reservoir of baryons for galaxy haloes.

Scale coupling in Richtmyer-Meshkov flows induced by strong shocks

We perform the first systematic study of the nonlinear evolution and scale coupling in Richtmyer-Meshkov (RM) flows induced by strong shocks. The smoothed particle hydrodynamics code (SPHC) is employed to ensure accurate shock capturing, interface tracking and accounting for the dissipation processes. We find that in strong-shock-driven RMI the background motion is supersonic. The amplitude of the initial perturbation strongly influences the flow evolution and the interfacial mixing that can be sub-sonic or supersonic. At late times the flow remains laminar rather than turbulent, and RM bubbles flatten and decelerate. In the fluid bulk, reverse cumulative jets appear and “hot spots” are formed—local heterogeneous microstructures with temperature substantially higher than that in the ambient. Our numerical simulations agree with the zero-order, linear, weakly nonlinear, and highly nonlinear theoretical analyses as well as with the experiments and suggest that the evolution of RMI is a multi-scale and heterogeneous process with a complicated character of scale coupling.

Cosmological simulations using gcmhd+

Radio observations of galaxy clusters show that the intra cluster medium is permeated by \mu G magnetic fields. The origin and evolution of these cosmological magnetic fields is currently not well understood and so their impact on the dynamics of structure formation is not known. Numerical simulations are required to gain a greater understanding and produce predictions for the next generation of radio telescopes. We present the galactic chemodynamics smoothed particle magnetohydrodynamic (SPMHD) code (GCMHD+), which is an MHD implementation for the cosmological smoothed particle hydrodynamic code GCD+. The results of 1, 2 and 3 dimensional tests are presented and the performance of the code is shown relative to the ATHENA grid code. GCMHD+ shows good agreement with the reference solutions produced by ATHENA. The code is then used to simulate the formation of a galaxy cluster with a simple primordial magnetic field embedded in the gas. A homogeneous seed field of 10^-11 G is amplified by a factor of 10^3 during the formation of the cluster. The results show good agreement with the profiles found in other magnetic cluster simulations of similar resolution.

Resolving high Reynolds numbers in smoothed particle hydrodynamics simulations of subsonic turbulence

Abstract Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For smoothed particle hydrodynamics (SPH) with constant artificial viscosity coefficient α, it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number — compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with α= 1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer & Springel to find agreement between the moving-mesh code arepo and the gadget SPH code on simulations of driven, subsonic (v∼ 0.3cs) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing α away from shocks.

ACCRETION DISKS AROUND KICKED BLACK HOLES: POST-KICK DYNAMICS

Numerical calculations of merging black hole binaries indicate that asymmetric emission of gravitational radiation can kick the merged black hole at up to thousands of km/s, and a number of systems have been observed recently whose properties are consistent with an active galactic nucleus containing a supermassive black hole moving with substantial velocity with respect to its broader accretion disk. We study here the effect of an impulsive kick delivered to a black hole on the dynamical evolution of its accretion disk using a smoothed particle hydrodynamics code, focusing attention on the role played by the kick angle with respect to the orbital angular momentum vector of the pre-kicked disk. We find that for more vertical kicks, for which the angle between the kick and the normal vector to the disk $\theta\lesssim 30^\circ$, a gap remains present in the inner disk, in accordance with the prediction from an analytic collisionless Keplerian disk model, while for more oblique kicks with $\theta\gtrsim 45^\circ$, matter rapidly accretes toward the black hole. There is a systematic trend for higher potential luminosities for more oblique kick angles for a given black hole mass, disk mass and kick velocity, and we find large amplitude oscillations in time in the case of a kick oriented $60^\circ$ from the vertical.

Numerical simulation of lava flow using a GPU SPH model

A smoothed particle hydrodynamics (SPH) method for lava-flow modeling was implemented on a graphical processing unit (GPU) using the compute unified device architecture (CUDA) developed by NVIDIA. This resulted in speed-ups of up to two orders of magnitude. The three-dimensional model can simulate lava flow on a real topography with free-surface, non-Newtonian fluids, and with phase change. The entire SPH code has three main components, neighbor list construction, force computation, and integration of the equation of motion, and it is computed on the GPU, fully exploiting the computational power. The simulation speed achieved is one to two orders of magnitude faster than the equivalent central processing unit (CPU) code. This GPU implementation of SPH allows high resolution SPH modeling in hours and days, rather than in weeks and months, on inexpensive and readily available hardware.

Smoothed particle magnetohydrodynamics with a Riemann solver and the method of characteristics

In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the interaction between particles, we solve a nonlinear Riemann problem with magnetic pressure for compressive waves and apply the method of characteristics for Alfv{\'e}n waves. An extensive series of MHD test calculations is performed. In all test calculations, we compare the results of our SPH code with those of a finite-volume method with an approximate Riemann solver, and confirm excellent agreement.

Smoothed particle hydrodynamics simulations of black hole accretion: a step to model black hole feedback in galaxies

(Abridged) We test how accurately the smoothed particle hydrodynamics (SPH) numerical technique can follow spherically-symmetric Bondi accretion. Using the 3D SPH code GADGET-3, we perform simulations of gas accretion onto a central supermassive black hole (SMBH) of mass 10^8 M_sun within the radial range of 0.1 - 200 pc. We carry out simulations without and with radiative heating by a central X-ray corona and radiative cooling. For an adiabatic case, the radial profiles of hydrodynamical properties match the Bondi solution, except near the inner and outer radius of the computational domain. We find that adiabatic Bondi accretion can be reproduced for durations of a few dynamical times at the Bondi radius, and for longer times if the outer radius is increased. With radiative heating and cooling included, the spherically accreting gas takes a longer time to reach a steady-state than the adiabatic Bondi accretion runs, and in some cases does not reach a steady-state even within several hundred dynamical times. We find that artificial viscosity in the GADGET code causes excessive heating near the inner radius, making the thermal properties of the gas inconsistent with a physical solution. This overheating occurs typically only in the supersonic part of the flow, so that it does not affect the mass accretion rate. We see that increasing the X-ray luminosity produces a lower central mass inflow rate, implying that feedback due to radiative heating is operational in our simulations. With a sufficiently high X-ray luminosity, the inflowing gas is radiatively heated up, and an outflow develops. We conclude that the SPH simulations can capture the gas dynamics needed to study radiative feedback provided artificial viscosity alters only highly supersonic part of the inflow.

On the migration of smooth particle hydrodynamic formulation in Cartesian coordinates to the axisymmetric formulation

The smooth particle hydrodynamic (SPH) method has been extended for application to large deformation problems such as high velocity impacts by including the effect of material strength. This paper presents a simple modification of the kernel function that allows the SPH formulation in Cartesian coordinates to be migrated into an axisymmetric formulation. The proposed procedure is first applied to analyse transient deformations of a cylindrical rod impacting a rigid wall (Taylor impact test). A good agreement with published experimental data for the deformed shape is obtained. A sensitivity study of the key parameters required in the SPH formulation is conducted to provide better insight into the SPH modelling approach. Impacts between two bodies at high speed have also been simulated using an axisymmetric SPH code.

RADIATION-DRIVEN IMPLOSION AND TRIGGERED STAR FORMATION

We present simulations of initially stable isothermal clouds exposed to ionising radiation from a discrete external source, and identify the conditions that lead to radiatively driven implosion and star formation. We use the Smoothed Particle Hydrodynamics code SEREN and an HEALPix-based photo-ionisation algorithm to simulate the propagation of the ionising radiation and the resulting dynamical evolution of the cloud. We find that the incident ionising flux, $\Phi_{_{\rm LyC}}$, is the critical parameter determining the cloud evolution. At moderate fluxes, a large fraction of the cloud mass is converted into stars. As the flux is increased, the fraction of the cloud mass that is converted into stars and the mean masses of the individual stars both decrease. Very high fluxes simply disperse the cloud. Newly-formed stars tend to be concentrated along the central axis of the cloud (i.e. the axis pointing in the direction of the incident flux). For given cloud parameters, the time, $t_{_\star}$, at which star formation starts is proportional to $\Phi_{_{\rm LyC}}^{-1/3}$. The pattern of star formation found in the simulations is similar to that observed in bright-rimmed clouds.

GPUs, a New Tool of Acceleration in CFD: Efficiency and Reliability on Smoothed Particle Hydrodynamics Methods

Smoothed Particle Hydrodynamics (SPH) is a numerical method commonly used in Computational Fluid Dynamics (CFD) to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs) or Graphics Processor Units (GPUs), a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA) of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability.

Flow-driven cloud formation and fragmentation: results from Eulerian and Lagrangian simulations

The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian Smoothed Particle Hydrodynamics (SPH) code VINE and the Eulerian grid code Proteus. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydro-dynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300K. For clumps more massive than 1 Msun/pc, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of magnitude smaller than their relative motion, rendering it subsonic with respect to the internal sound speed of the clumps, but supersonic as seen by an external observer. For the SPH simulations most of the cold gas resides at temperatures below 100K, while the grid-based models show an additional, substantial component between 100 and 300K. Independently of the numerical method our models confirm that converging flows of warm neutral gas fragment rapidly and form high-density, low-temperature clumps as possible seeds for star formation.

Numerical simulation of compressive failure of heterogeneous rock-like materials using SPH method

A novel numerical approach based on the mesh-free smoothed particle hydrodynamics (SPH) method is developed to simulate the failure of brittle heterogeneous materials by tracing the propagation of the microscopic cracks as well as the macromechanical behaviors. An elasto-plastic damage model based on the extension of the unified twin shear strength (UTSS) criterion is adopted to reflect the strength behavior of the materials. A statistical approach is applied to model the material heterogeneity. The developed SPH code is used to simulate the heterogeneous rock-like material compressive failure under the uniaxial and biaxial loading conditions. The influences of the material heterogeneity as well as the confining loading conditions are investigated. Results demonstrate that the developed program is effective and promising for more complex applications.

Ionization feedback in star formation simulations: the role of diffuse fields

We compare the three-dimensional gas temperature distributions obtained by a dedicated radiative transfer and photoionisation code, MOCASSIN, against those obtained by the recently-developed Smooth Particle Hydrodynamics (SPH) plus ionisation code iVINE for snapshots of an hydrodynamical simulation of a turbulent interstellar medium (ISM) irradiated by a nearby O star. Our tests demonstrate that the global ionisation properties of the region are correctly reproduced by iVINE, hence validating further application of this code to the study of feedback in star forming regions. However we highlight potentially important discrepancies in the detailed temperature distribution. In particular we show that in the case of highly inhomogenous density distributions the commonly employed on-the-spot (OTS) approximation yields unrealistically sharp shadow regions which can affect the dynamical evolution of the system. We implement a simple strategy to include the effects of the diffuse field in future calculations, which makes use of physically motivated temperature calibrations of the diffuse-field dominated regions and can be readily applied to similar codes. We find that while the global qualitative behaviour of the system is captured by simulations with the OTS approximation, the inclusion of the diffuse field in iVINE (called DiVINE) results in a stronger confinement of the cold gas, leading to denser and less coherent structures. This in turn leads to earlier triggering of star formation. We confirm that turbulence is being driven in simulations that include the diffuse field, but the efficiency is slightly lower than in simulations that use the OTS approximation.

RpSPH: a novel smoothed particle hydrodynamics algorithm

We suggest a novel discretisation of the momentum equation for Smoothed Particle Hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force in respect to the local pressure. It respects Newtons first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newtons third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension, and unphysical scattering of different mass particles found for standard SPH. At the same time it uses fewer computational operations. and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently one can also obtain unphysical solutions particularly at low resolutions.

Neighbour lists in smoothed particle hydrodynamics

AbstractSince smoothed particle hydrodynamics (SPH) is based on interactions with the closer neighbouring particles, implementing the neighbour list is a key point in terms of the high performance of the code. The efficiency of the method depends directly on how to build and use the neighbour list. In the present work, the available searching algorithms for SPH codes are analyzed. Different gridding algorithms are evaluated, the gains in efficiency obtained from reordering of particles is investigated and the cell‐linked list and Verlet list methods are studied to create the neighbour list. Furthermore, an innovative searching procedure based on a dynamic updating of the Verlet list is proposed. The efficiency of the algorithms is analyzed in terms of computational time and memory requirements. Copyright © 2010 John Wiley & Sons, Ltd.

Long-duration gamma-ray bursts: hydrodynamic instabilities in collapsar discs

We present 3D numerical simulations of the early evolution of long-duration gamma-ray bursts in the collapsar scenario. Starting from the core-collapse of a realistic progenitor model, we follow the formation and evolution of a central black hole and centrifugally balanced disk. The dense, hot accretion disk produces freely-escaping neutrinos and is hydrodynamically unstable to clumping and to forming non-axisymmetric (m=1, 2) modes. We show that these spiral structures, which form on dynamical timescales, can efficiently transfer angular momentum outward and can drive the high required accretion rates (>=0.1-1 M_sun) for producing a jet. We utilise the smoothed particle hydrodynamics code, Gadget-2, modified to implement relevant microphysics, such as cooling by neutrinos, a plausible treatment approximating the central object and relativistic effects. Finally, we discuss implications of this scenario as a source of energy to produce relativistically beamed gamma-ray jets.

START: smoothed particle hydrodynamics with tree-based accelerated radiative transfer

We present a novel radiation hydrodynamics code, START, which is a smoothed particle hydrodynamics (SPH) scheme coupled with accelerated radiative transfer. The basic idea for the acceleration of radiative transfer is parallel to the tree algorithm that is hitherto used to speed up the gravitational force calculation in an N-body system. It is demonstrated that the radiative transfer calculations can be dramatically accelerated, where the computational time is scaled as Np log Ns for Np SPH particles and Ns radiation sources. Such acceleration allows us to readily include not only numerous sources but also scattering photons, even if the total number of radiation sources is comparable to that of SPH particles. Here, a test simulation is presented for a multiple source problem, where the results with START are compared to those with a radiation SPH code without tree-based acceleration. We find that the results agree well with each other if we set the tolerance parameter as < 1.0, and then it demonstrates that START can solve radiative transfer faster without reducing the accuracy. One of important applications with START is to solve the transfer of diffuse ionizing photons, where each SPH particle is regarded as an emitter. To illustrate the competence of START, we simulate the shadowing effect by dense clumps around an ionizing source. As a result, it is found that the erosion of shadows by diffuse recombination photons can be solved. Such an effect is of great significance to reveal the cosmic reionization process.