We present an investigation on effect of the ion-neutral (or ambipolar) diffusion heating rate on thermal phases of a molecular cloud. We use the modeling of ambipolar diffusion with two-fluid smoothed particle hydrodynamics, as discussed by Nejad-Asghar & Molteni. We take into account the ambipolar drift heating rate on the net cooling function of the molecular clouds, and we investigate the thermal phases in a self-gravitating magnetized one dimensional slab. The results show that the isobaric thermal instability criterion is satisfied in the outer parts of the cloud, thus, these regions are thermally unstable while the inner part is stable. This feature may be responsible for the planet formation in the outer parts of a collapsing molecular cloud and/or may also be relevant for the formation of star forming dense cores in the clumps.
We adapt the Smoothed-Particle Hydrodynamics technique to allow a multiphase fluid in which SPH particles of widely differing density may be freely intermixed. Applications include modelling of galaxy formation and cooling flows.
We summarize the ideas that led to the Adaptive Smoothed Particle Hydrodynamics (ASPH) algorithm, with anisotropic smoothing and shock-tracking. We then identify a serious new problem for SPH simulations with shocks and radiative cooling --- false cooling --- and discuss a possible solution based on the shock-tracking ability of ASPH.
Isothermal and adiabatic shocks, which are produced from fast expansion of the gas, is simulated with smoothed particle hydrodynamics (SPH). The results are compared with the analytic solutions. The algorithm of the program is explained and the package, which is written in Fortran, is presented in the appendix of this paper. It is possible to change (to complete) the program for a wide variety of applications ranging from astrophysics to fluid mechanics.
Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar interactions, including collisions between main sequence stars and the coalescence of compact binaries.
We revisit the modeling of ion-neutral (or ambipolar) diffusion with two fluid smoothed particle hydrodynamics, as discussed by Hosking & Whitworth. Some parts of the technique are optimized to testify the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating layer. The frictional heating by ambipolar diffusion is examined, and its effect on fragmentation of the layer is studied. The results are compared to the thermal phases of instability as obtained by Nejad-Asghar.
A new method for the inclusion of ionizing radiation from uniform radiation fields into 3D Smoothed Particle Hydrodynamics (SPHI) simulations is presented. We calculate the optical depth for the Lyman continuum radiation from the source towards the SPHI particles by ray-tracing integration. The time-dependent ionization rate equation is then solved locally for the particles within the ionizing radiation field. Using test calculations, we explore the numerical behaviour of the code with respect to the implementation of the time-dependent ionization rate equation. We also test the coupling of th…
We present results of numerical simulation of thin accretion disks and winds. We use the Smoothed Particle Hydrodynamics (SPH) technique for this purpose. We show that the simulation agrees very well with the recent theoretical work on the shock formation. The most significant conclusion is that shocks in an inviscid flow are extremely stable. For the first time, our work also removes the ambiguity in terms of the location and stability of shocks in adiabatic flows.
Smoothed Particle Hydrodynamics is reformulated in terms of the convolution of the original hydrodynamics equations, and the new evolution equations for the particles are derived. The same evolution equation of motion is also derived using a new action principle. The force acting on each particle is determined by solving the Riemann problem. The use of the Riemann Solver strengthens the method, making it accurate for the study of phenomena with strong shocks. The prescription for the variable smoothing length is shown. These techniques are implemented in strict conservation form. The results o…
The artificial viscosity is reconsidered in smoothed particle hydrodynamics to prevent inter-particle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan's standard artificial viscosity are considered as time variable, and a restriction on them is proposed such that avoiding the undesired effects in the subsonic regions. The shock formation in adiabatic and isothermal cases are used to study the ability of this modified artificial viscosity recipe. The computer experiments show that the proposal appears to work and the accuracy of this restriction is accep…
We describe a new, faster implicit algorithm for solving the radiation hydrodynamics equations in the flux-limited diffusion approximation for smoothed particle hydrodynamics. This improves on the method elucidated in Whitehouse & Bate by using a Gauss-Seidel iterative method rather than iterating over the exchange of energy between pairs of particles. The new algorithm is typically many thousands of times faster than the old one, which will enable more complex problems to be solved. The new algorithm is tested using the same tests performed by Turner & Stone for ZEUS-2D, and repeated by White…
We present a new fast algorithm which allows the simulation of ionising radiation emitted from point sources to be included in high-resolution three-dimensional smoothed particle hydrodynamics simulations of star cluster formation. We employ a Strömgren volume technique in which we use the densities of particles near the line-of-sight between the source and a given target particle to locate the ionisation front in the direction of the target. Along with one--dimensional tests, we present fully three--dimensional comparisons of our code with the three--dimensional Monte-Carlo radiative transfer…
We provide a description of the SNSPH code--a parallel 3-dimensional radiation hydrodynamics code implementing treecode gravity, smooth particle hydrodynamics, and flux-limited diffusion transport schemes. We provide descriptions of the physics and parallelization techniques for this code. We present performance results on a suite of code tests (both standard and new), showing the versatility of such a code, but focusing on what we believe are important aspects of modeling core-collapse supernovae.
We describe the implementation and testing of a smoothed particle hydrodynamics (SPH) code that solves the equations of radiation hydrodynamics in the flux-limited diffusion (FLD) approximation. The SPH equations of radiation hydrodynamics for an explicit integration scheme are derived and tested. We also discuss the implementation of an implicit numerical scheme for solving the radiation equations that allows the system to be evolved using timesteps much longer than the explicit radiation timestep. The code is tested on a variety of one-dimensional radiation hydrodynamics problems including r…
We study the problem of the appropriate choice of the interpolating kernel to be used in the evaluation of gradients of functions. Such interpolation technique is often used in applications, e.g. it is typical for Smoothed Particle Hydrodynamics (SPH). We propose a minimization procedure for selecting kernels in n-dimensions, in the class of regular, normalizable, symmetric functions having finite moments up to a sufficiently high order; the method is valid when the kernel width is position-dependent and allows to recover conservation laws at the same order of approximation that SPH, as interp…
This paper presents SPLASH, a publicly available interactive visualisation tool for Smoothed Particle Hydrodynamics (SPH) simulations. Visualisation of SPH data is more complicated than for grid-based codes because the data is defined on a set of irregular points and therefore requires a mapping procedure to a two dimensional pixel array. This means that, in practise, many authors simply produce particle plots which offer a rather crude representation of the simulation output. Here we describe the techniques and algorithms which are utilised in SPLASH in order to provide the user with a fast, …
We have been constructed a brand-new radiation hydrodynamics solver based upon Smoothed Particle Hydrodynamics (SPH), which works on parallel computer system. The code is designed to investigate the formation and evolution of the first generation objects at $z \gtrsim 10$, where the radiative feedback from various sources play important roles. The code can compute the fraction of chemical species e, H$^+$, H, H$^-$, H$_2$, and H$_2^+$ by fully implicit time integration. It also can deal with multiple sources of ionizing radiation, as well as the radiation at Lyman-Werner band. We compare the r…
We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing suitable Lagrangian time evolution variables, from which the generic fluid variables rest-mass density, 3-velocity, and thermodynamic pressure have to be determined. We present the corresponding equations for an ideal gas and show the existence and uniqueness of the solution. On the basis of the Lagrangian formulation we have developed a three-dimensional g…
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 (ICF, -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 …
A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n is analyzed in the context of the smoothed-particle hydrodynamics (SPH) technique. The behaviour of these kernels for several values of the parameter n has been studied either analytically as well as numerically in connection with several tests carried out in two dimensions. The main advantage of this kernel relies in its flexibility because for n=3 it is similar to the standard widely used cubic-spline, whereas for n>3 the interpolating function becomes more centrally condensed, being well suited to track discontinui…
Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one and two dimensional flows) using Smoothed Particle Hydrodynamics. We discover that for a large region of the parameter space, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock disappears. In the intermediate viscosity the disc oscillates very significantly in viscous time-scale. Our simulations ind…
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 which 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…
A new Chemo -- Dynamical Smoothed Particle Hydrodynamic (CD -- SPH) code is presented. The disk galaxy is described as a multi -- fragmented gas and star system, embedded into the cold dark matter halo. The star formation (SF) process, SNII, SNIa and PN events as well as chemical enrichment of gas have been considered within the framework of standard SPH model. Using this model we try to describe the dynamical and chemical evolution of triaxial disk -- like galaxies. It is found that such approach provides a realistic description of the process of formation, chemical and dynamical evolution of…
We introduce a simple and efficient algorithm for diffusion in smoothed particle hydrodynamics (SPH) simulations and apply it to the problem of chemical mixing. Based on the concept of turbulent diffusion, we link the diffusivity of a pollutant to the local physical conditions and can thus resolve mixing in space and time. We apply our prescription to the evolution of an idealized supernova remnant and find that we can model the distribution of heavy elements without having to explicitly resolve hydrodynamic instabilities in the post-shock gas. Instead, the dispersal of the pollutant is implic…
We present a practical guide to Smoothed Particle Hydrodynamics (\SPH) and its application to astrophysical problems. Although remarkably robust, \SPH\ must be used with care if the results are to be meaningful since the accuracy of \SPH\ is sensitive to the arrangement of the particles and the form of the smoothing kernel. In particular, the initial conditions for any \SPH\ simulation must consist of particles in dynamic equilibrium. We describe some of the numerical difficulties that may be encountered when using \SPH, and how these may be overcome. Through our experience in using \SPH\ code…
We present the results of a series of calculations studying the collapse of molecular cloud cores performed using a three-dimensional smoothed particle hydr odynamics code with radiative transfer in the flux-limited diffusion approximation. The opacities and specific heat capacities are identical for each calculation. However, we find that the temperature evolution during the simulations varies significantly when starting from different initial conditions. Even spherically-symmetric clouds with different initial densities show markedly different development. We conclude that simple barotropic …
DQ Herculis was the Summer 1997 WET northern-hemisphere primary target. The O-C phase diagram of the 71-s signal reveals out-of-eclipse phase variations resulting from the self eclipses of a nearly edge-on, non-axisymmetric disc. We work the forward problem of simulating DQ Herculis numerically using the method of smoothed particle hydrodynamics (SPH), and from the time-averaged structure calculate the O-C phase variations as a function of inclination angle. The WET and SPH O-C phase variations match to a remarkable degree, and suggest a system inclination in the range 89.5 to 89.7 degrees.
Smoothed Particle Hydrodynamics (SPH) is a unique numerical method widely used for astrophysical problems since it involves no spatial grid. Rather, fluid quantities are carried by a set of Lagrangian `particles' which move with the flow, meaning that complicated dynamics and asymmetric phenomena are treated with ease. Since adaptivity is a built-in feature of the method there is no need to resort to complicated additional mesh refinement procedures. In this chapter we have undertaken a thorough review of the SPH method in order to develop a sufficiently accurate method which can be applied to…
We have developed Remote-GRAPE, a subroutine library to use the special purpose computer GRAPE-3A. The GRAPE-3A can efficiently calculate gravitational force between particles, and construct neighbor lists. All other calculations are performed on the host workstation (WS) which is directly connected to GRAPE. The use of GRAPE for Smoothed Particle Hydrodynamics (GRAPE-SPH) can in principle greatly speed up the calculations on WS. However the current bottleneck of GRAPE-SPH is that its performance is limited by the speed of the host WS. To solve this problem, we implement Remote-GRAPE; it allow…
We present an analysis of star formation and feedback recipes appropriate for galactic smoothed particle hydrodynamics simulations. Using an isolated Milky Way-like galaxy, we constrain these recipes based on well-established observational results. Our star formation recipe is based on that of Katz (1992) with the additional inclusion of physically motivated supernova feedback recipes. We propose a new feedback recipe in which type II supernovae are modelled using an analytical treatment of blastwaves. With this feedback mechanism and a tuning of other star formation parameters, the star forma…
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 (2007), and flux limited diffusion (e.g. Mayer et al 2007). 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, whic…
Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of non-hydrodynamical nature. Under this approach, SPH is viewed as strictly an interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogeneous sound speed and (2) Burgers equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite difference methods. It is sh…
We have performed a series of systematic tests to evaluate the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numerical viscosity, and (iv) angular momentum transport. The results are useful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by…
We have performed Smoothed Particle Hydrodynamics (SPH) simulations to study the time evolution of one and two protoplanets embedded in a protoplanetary accretion disc. We investigate accretion and migration rates of a single protoplanet depending on several parameters of the protoplanetary disc, mainly viscosity and scale height. Additionally, we consider the influence of a second protoplanet in a long time simulation and examine the migration of the two planets in the disc, especially the growth of eccentricity and chaotic behaviour. One aim of this work is to establish the feasibility of SP…
The heating of the ion-neutral (or ambipolar) diffusion may affect the thermal phases of the molecular clouds. We present an investigation on the effect of this heating mechanism in the thermal instability of the molecular clouds. A weakly ionized one dimensional slab geometry, which is allowed for self-gravity and ambipolar diffusion, is chosen to study its thermal phases. We use the thermodynamic evolution of the slab to obtain the regions where slab cloud becomes thermally unstable. We investigate this evolution using the model of ambipolar diffusion with two-fluid smoothed particle hydrody…
We present TRAPHIC, a novel radiative transfer scheme for Smoothed Particle Hydrodynamics (SPH) simulations. TRAPHIC is designed for use in simulations exhibiting a wide dynamic range in physical length scales and containing a large number of light sources. It is adaptive both in space and in angle and can be employed for application on distributed memory machines. The commonly encountered computationally expensive scaling with the number of light sources in the simulation is avoided by introducing a source merging procedure. The (time-dependent) radiative transfer equation is solved by tracin…
In recent years a handful of systems have been observed to show "negative" (nodal) superhumps, with periods slightly shorter than the orbital period. It has been suggested that these modes are a consequence of the slow retrograde precession of the line of nodes in a disk tilted with respect to the orbital plane. Our simulations confirm and refine this model: they suggest a roughly axisymmetric, retrogradely-precessing, tilted disk that is driven at a period slightly less than half the orbital period as the tidal field of the orbiting secondary encounters in turn the two halves of the disk abov…
We introduce SPHRAY, a Smoothed Particle Hydrodynamics (SPH) ray tracer designed to solve the 3D, time dependent, radiative transfer (RT) equations for arbitrary density fields. The SPH nature of SPHRAY makes the incorporation of separate hydrodynamics and gravity solvers very natural. SPHRAY relies on a Monte Carlo (MC) ray tracing scheme that does not interpolate the SPH particles onto a grid but instead integrates directly through the SPH kernels. Given initial conditions and a description of the sources of ionizing radiation, the code will calculate the non-equilibrium ionization state (HI…
The method of smoothed particle hydrodynamics (SPH) is developped appropriately for the study of relativistic heavy ion collision processes. In order to describe the flow of a high energy but low baryon number density fluid, the entropy is taken as the SPH base. We formulate the method in terms of the variational principle. Several examples show that the method is very promising for the study of hadronic flow in RHIC physics.
We analyse the performance of twelve different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and disc stability. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by differ…
We present a new 3D SPH code which solves the general relativistic field + hydrodynamics equations in the conformally flat approximation. Several test cases are considered to test different aspects of the code. We finally apply then the code to the coalescence of a neutron star binary system. The neutron stars are modeled by a polytropic equation of state (EoS) with adiabatic indices $Γ=2.0$, $Γ=2.6$ and $Γ=3.0$. We calculate the gravitational wave signals, luminosities and frequency spectra by employing the quadrupole approximation for emission and back reaction in the slow motion limit. In a…
