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In smoothed particle hydrodynamics (SPH) codes with a large number of particles, star formation as well as gas and metal restitution from dying stars can be treated statistically. This approach allows one to include detailed chemical evolution and gas re-ejection with minor computational effort. Here we report on a new statistical algorithm for star formation and chemical evolution, especially conceived for SPH simulations with large numbers of particles, and for parallel SPH codes.
For the sake of illustration, we also present two astrophysical simulations obtained with this algorithm, implemented into the Tree-SPH code by Lia & Carraro .
In the first simulation, we follow the formation of an individual disc-like galaxy, predict the final structure and metallicity evolution, and test resolution effects. In the second simulation we simulate the formation and evolution of a cluster of galaxies, to demonstrate the capabilities of the algorithm in investigating the chemo-dynamical evolution of galaxies and of the intergalactic medium in a cosmological context.  相似文献   

3.
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.  相似文献   

4.
A simple algorithm is presented which generates a lattice-like, regular spacing of smoothed particle hydrodynamics (SPH) particles in discs, with any prescribed density gradient. Using this for comparison we demonstrate the effect of Poisson noise on SPH estimates of density, pressure and viscous forces when calculated using randomly distributed particles. The standard deviation of density and pressure is typically increased by greater than an order of magnitude. In a disc with a Keplerian velocity profile, the effectiveness of the Balsara switch in reducing the shear component of SPH artificial viscosity is greatly enhanced when the particles are properly spaced, reducing the magnitude of viscosity by two orders of magnitude. Noise problems are exacerbated, not removed, by increasing the numbers of SPH particles, if the number of neighbours used is kept constant. However, comparison of the evolution of a disc created using perfectly spaced particles and a disc with identical parameters but randomly placed particles, reveals very similar results. Although there are subtle differences in the evolution, and the smooth disc takes longer to begin developing structure, in both cases the identical number of objects is created by gravitational collapse. SPH disc simulations do not depend on initial density disturbances to evolve objects by gravitational collapse, which gives added credence to the validity of the results. It also appears that complicated disc settling procedures are unnecessary.  相似文献   

5.
We describe similarity solutions that characterize the collapse of collisional gas on to scale-free perturbations in an Einstein–de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the assumption that the cooling function is a power law of density and temperature, Λ( T , ρ )∝ ρ 3/2 T . We use these results to test the ability of smooth particle hydrodynamics (SPH) techniques to follow the collapse and accretion of shocked, rapidly cooling gas in a cosmological context. Our SPH code reproduces the analytical results very well in cases that include or exclude radiative cooling. No substantial deviations from the predicted central mass accretion rates or from the temperature, density and velocity profiles are observed in well-resolved regions inside the shock radius. This test problem lends support to the reliability of SPH techniques to model the complex process of galaxy formation.  相似文献   

6.
In this paper, we describe an adaptive softening length formalism for collisionless N -body and self-gravitating smoothed particle hydrodynamics (SPH) calculations which conserves momentum and energy exactly. This means that spatially variable softening lengths can be used in N -body calculations without secular increases in energy. The formalism requires the calculation of a small additional term to the gravitational force related to the gradient of the softening length. The extra term is similar in form to the usual SPH pressure force (although opposite in direction) and is therefore straightforward to implement in any SPH code at almost no extra cost. For N -body codes, some additional cost is involved as the formalism requires the computation of the density through a summation over neighbouring particles using the smoothing kernel. The results of numerical tests demonstrate that, for homogeneous mass distributions, the use of adaptive softening lengths gives a softening which is always close to the 'optimal' choice of fixed softening parameter, removing the need for fine-tuning. For a heterogeneous mass distribution (as may be found in any large-scale N -body simulation), we find that the errors on the least-dense component are lowered by an order of magnitude compared to the use of a fixed softening length tuned to the densest component. For SPH codes, our method presents a natural and an elegant choice of softening formalism which makes a small improvement to both the force resolution and the total energy conservation at almost zero additional cost.  相似文献   

7.
For simulations of fluid dynamics in astrophysics, physical viscosity and diffusion are typically neglected. However, in this high Reynolds number regime, real fluids become highly turbulent and turbulent processes mediate substantial transport of momentum and heat that is diffusive in nature. In the absence of models for these processes, code-dependent numerical effects dominate how diffusion operates and may lead to physically incorrect simulation results. We highlight the qualitative difference in these numerical effects for smooth particle hydrodynamics (SPH) and grid-based Eulerian codes using two test problems: a buoyant gas bubble and gas in a galaxy cluster. Grid codes suffer from numerical diffusion in the absence of explicit terms, and small-scale diffusion of heat is completely absent in the Lagrangian SPH method. We find that SPH with heat diffusion added at a level similar to that expected from turbulence diffusion generates more physically appealing results. These results suggest, but do not confirm, that a flat entropy core is to be expected for gas in an idealized galaxy cluster (i.e. one without physics beyond that of a non-radiating gas). A goal of this work is thus to draw attention to the as yet unfulfilled need for models of turbulent diffusive processes in compressible gases in astrophysics.  相似文献   

8.
We describe an smooth particle hydrodynamics (SPH) model for chemical enrichment and radiative cooling in cosmological simulations of structure formation. This model includes: (i) the delayed gas restitution from stars by means of a probabilistic approach designed to reduce the statistical noise and, hence, to allow for the study of the inner chemical structure of objects with moderately high numbers of particles; (ii) the full dependence of metal production on the detailed chemical composition of stellar particles by using, for the first time in SPH codes, the   Q ij   matrix formalism that relates each nucleosynthetic product to its sources and (iii) the full dependence of radiative cooling on the detailed chemical composition of gas particles, achieved through a fast algorithm using a new metallicity parameter ζ( T ) that gives the weight of each element on the total cooling function. The resolution effects and the results obtained from this SPH chemical model have been tested by comparing its predictions in different problems with known theoretical solutions. We also present some preliminary results on the chemical properties of elliptical galaxies found in self-consistent cosmological simulations. Such simulations show that the above ζ-cooling method is important to prevent an overestimation of the metallicity-dependent cooling rate, whereas the   Q ij   formalism is important to prevent a significant underestimation of the [α/Fe] ratio in simulated galaxy-like objects.  相似文献   

9.
We describe and demonstrate a method for increasing the resolution locally in a Smoothed Particle Hydrodynamic (SPH) simulation, by splitting particles. We show that in simulations of self-gravitating collapse (of the sort that are presumed to occur in star formation) the method is stable, and affords great savings in computer time and memory. When applied to the standard Boss & Bodenheimer test – which has been shown to depend critically on fulfilment of the Jeans Condition – the results are comparable both with those obtained using Adaptive Mesh Refinement, and with those obtained using a standard high-resolution SPH simulation, but they are achieved with considerably less computational resource. Further development and testing is required before the method can safely be applied to more general flows.  相似文献   

10.
Toy Stars are gas masses where the compressibility is treated without approximations but gravity is replaced by a force which, for any pair of masses, is along their line of centres and proportional to their separation. They provide an invaluable resource for testing the suitability of numerical codes for astrophysical gas dynamics. In this paper, we derive the equations for both small-amplitude oscillations and non-linear solutions for rotating and pulsating Toy Stars in two dimensions, and show that the solutions can be reduced to a small number of ordinary differential equations. We compare the accurate solutions of these equations with Smoothed Particle Hydrodynamics (SPH) simulations. The two-dimensional Toy Star solutions are found to provide an excellent benchmark for SPH algorithms, highlighting many of the strengths and also some weaknesses of the method.  相似文献   

11.
Modelling planets is done for two main reasons – the first to further understanding of their internal structure and the second to provide models to explore astrophysical situations in which planets play a role. For the latter reason, the requirements on accuracy are less severe, although the planet must be realistic in its major features. A numerical model of a layered giant planet is developed with an iron core, a silicate mantle, an ice region and a hydrogen–helium atmosphere. The Tillotson equation of state is used and examples of two model planets are given, one reproducing the mass and radius of Jupiter quite closely and the other with two Jupiter masses. Transferring these results into a smoothed particle hydrodynamics (SPH) model presents two main difficulties. A uniform distribution of SPH points leads to too few points representing the non-atmospheric component. It is shown that using a distorted lattice enables the core + silicate + ice to be represented by several hundred points so that the evolution of these regions can be followed in detail. Another difficulty concerns the density discontinuities attendant on a layered structure. Density estimates of SPH points are either too large or too small near material interfaces leading to unrealistic pressure gradients and, consequently, to large and unphysical local forces. Algorithms are described for avoiding this difficulty both at material interfaces and near the surface of the planet. In some astrophysical situations involving SPH-modelled planets, the main bulk of the planet is so opaque that internal heat transfer can be neglected. However, surface regions should radiate and a convenient way for including radiation from a planetary surface is described.  相似文献   

12.
Variational principles for relativistic smoothed particle hydrodynamics   总被引:1,自引:0,他引:1  
In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.  相似文献   

13.
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Using the multi-band photometric data of all five CANDELS (Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey) fields and the near-infrared (F125W and F160W) high-resolution images of HST WFC3 (Hubble Space Telescope Wide Field Camera 3), a quantitative study of morphology and structure of mass-selected galaxies is presented. The sample includes 8002 galaxies with a redshift 1 < z < 3 and stellar mass M*> 1010M. Based on the Convolutional Neural Network (ConvNet) criteria, we classify the sample galaxies into SPHeroids (SPH), Early-Type Disks (ETD), Late-Type Disks (LTD), and IRRegulars (IRR) in different redshift bins. The findings indicate that the galaxy morphology and structure evolve with redshift up to z ~ 3, from irregular galaxies in the high-redshift universe to the formation of the Hubble sequence dominated by disks and spheroids. For the same redshift interval, the median values of effective radii (re) of different morphological types are in a descending order: IRR, LTD, ETD, and SPH. But for the Sérsic index (n), the order is reversed (SPH, ETD, LTD, and IRR). In the meantime, the evolution of galaxy size (re) with the redshift is explored for the galaxies of different morphological types, and it is confirmed that their size will enlarge with time. However, such a phenomenon is not found in the relations between the redshift (1 < z < 3) and the mean axis ratio (b/a), as well as the Sérsic index (n).  相似文献   

16.
In an effort to study the halo globular clusters we perform a simulation of inhomogeneous halo collapse using a SPH/N-body code. We include dark matter particles, (cooling) gas, and stars. Supernova feedback is included as a heat source for the gas in the local environment of star forming regions. We find this model cannot reproduce the age distribution and spatial distribution of halo globular clusters. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

17.
18.
To measure the onset of mass transfer in eccentric binaries, we have developed a two-phase smoothed particle hydrodynamics (SPH) technique. Mass transfer is important in the evolution of close binaries, and a key issue is to determine the separation at which mass transfer begins. The circular case is well understood and can be treated through the use of the Roche formalism. To treat the eccentric case, we use a newly developed two-phase system. The body of the donor star is made up from high-mass water particles, whilst the atmosphere is modelled with low-mass oil particles. Both sets of particles take part fully in SPH interactions. To test the technique, we model circular mass-transfer binaries containing a  0.6 M  donor star and a  1 M  white dwarf; such binaries are thought to form cataclysmic variable (CV) systems. We find that we can reproduce a reasonable CV mass-transfer rate, and that our extended atmosphere gives a separation that is too large by approximately 16 per cent, although its pressure scale height is considerably exaggerated. We use the technique to measure the semimajor axis required for the onset of mass transfer in binaries with a mass ratio of   q = 0.6  and a range of eccentricities. Comparing to the value obtained by considering the instantaneous Roche lobe at pericentre, we find that the radius of the star required for mass transfer to begin decreases systematically with increasing eccentricity.  相似文献   

19.
We describe a new implementation of a parallel TreeSPH code with the aim of simulating galaxy formation and evolution. The code has been parallelized using shmem , a Cray proprietary library to handle communications between the 256 processors of the Silicon Graphics T3E massively parallel supercomputer hosted by the Cineca Super-computing Center (Bologna, Italy). 1
The code combines the smoothed particle hydrodynamics (SPH) method for solving hydrodynamical equations with the popular Barnes & Hut tree-code to perform gravity calculation with an N ×log  N scaling, and it is based on the scalar TreeSPH code developed by Carraro et al. Parallelization is achieved by distributing particles along processors according to a workload criterion.
Benchmarks, in terms of load balance and scalability, of the code are analysed and critically discussed against the adiabatic collapse of an isothermal gas sphere test using 2×104 particles on 8 processors. The code results balance at more than the 95 per cent level. Increasing the number of processors, the load balance slightly worsens. The deviation from perfect scalability for increasing number of processors is almost negligible up to 32 processors. Finally, we present a simulation of the formation of an X-ray galaxy cluster in a flat cold dark matter cosmology, using 2×105 particles and 32 processors, and compare our results with Evrard's P3M–SPH simulations.
Additionally we have incorporated radiative cooling, star formation, feedback from SNe of types II and Ia, stellar winds and UV flux from massive stars, and an algorithm to follow the chemical enrichment of the interstellar medium. Simulations with some of these ingredients are also presented.  相似文献   

20.
A new means of incorporating radiative transfer into smoothed particle hydrodynamics (SPH) is introduced, which builds on the success of two previous methods – the polytropic cooling approximation as devised by Stamatellos et al. and flux-limited diffusion. This hybrid method preserves the strengths of its individual components, while removing the need for atmosphere matching or other boundary conditions to marry optically thick and optically thin regions. The code uses a non-trivial equation of state to calculate temperatures and opacities of SPH particles, which captures the effects of H2 dissociation, H0 ionization, He0 and He+ ionization, ice evaporation, dust sublimation, molecular absorption, bound-free and free–free transitions and electron scattering. The method is tested in several scenarios, including (i) the evolution of a  0.07 M  protoplanetary disc surrounding a  0.5 M  star; (ii) the collapse of a  1 M  protostellar cloud and (iii) the thermal relaxation of temperature fluctuations in a static homogeneous sphere.  相似文献   

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