This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, ...showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several ‘urban myths’ regarding SPH, in particular the idea that one can simply increase the ‘neighbour number’ more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the
ndspmhd SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Downregulation of the expression of specific genes through RNA interference (RNAi), has been widely used for genetic research in insects. The method has relied on the injection of double-stranded RNA ...(dsRNA), which is not possible for practical applications in crop protection. By contrast, specific suppression of gene expression in nematodes is possible through feeding with dsRNA. This approach was thought to be unfeasible in insects, but recent results have shown that dsRNA fed as a diet component can be effective in downregulating targeted genes. More significantly, expression of dsRNA directed against suitable insect target genes in transgenic plants has been shown to give protection against pests, opening the way for a new generation of insect-resistant crops.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
In this paper we discuss the treatment of discontinuities in smoothed particle hydrodynamics (SPH) simulations. In particular we discuss the difference between integral and differential ...representations of the fluid equations in an SPH context and how this relates to the formulation of dissipative terms for the capture of shocks and other discontinuities.
This has important implications for many problems, in particular related to recently highlighted problems in treating Kelvin–Helmholtz instabilities across entropy gradients in SPH. The specific problems pointed out by Agertz et al. O. Agertz, B. Moore, J. Stadel, D. Potter, F. Miniati, J. Read, L. Mayer, A. Gawryszczak, A. Kravtsov, Å. Nordlund, F. Pearce, V. Quilis, D. Rudd, V. Springel, J. Stone, E. Tasker, R. Teyssier, J. Wadsley, R. Walder, Fundamental differences between SPH and grid methods, MNRAS 380 (2007) 963–978 are shown to be related in particular to the (lack of) treatment of contact discontinuities in standard SPH formulations which can be cured by the simple application of an artificial thermal conductivity term. We propose a new formulation of artificial thermal conductivity in SPH which minimises dissipation away from discontinuities and can therefore be applied quite generally in SPH calculations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
We present three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations investigating the dependence of the accretion rate on the disc thickness around an equal-mass, circular black hole ...binary system. We find that for thick/hot discs, with H/R ≳ 0.1, the binary torque does not prevent the gas from penetrating the cavity formed in the disc by the binary (in line with previous investigations). The situation drastically changes for thinner discs; in this case the mass accretion rate is suppressed, such that only a fraction (linearly dependent on H/R) of the available gas is able to flow within the cavity and accrete on to the binary. Extrapolating this result to the cold and thin accretion discs expected around supermassive black hole binary systems implies that this kind of system accretes less material than predicted so far, with consequences not only for the electromagnetic and gravitational waves emissions during the late inspiral phase but also for the recoil speed of the black hole formed after binary coalescence, thus influencing also the evolutionary path both of the binary and of the host galaxy. Our results, being scale-free, are also applicable to equal-mass, circular binaries of stellar mass black holes, such as the progenitor of the recently discovered gravitational wave source GW150914.
In this paper we analyse the propagation of warps in protostellar circumbinary discs. We use these systems as a test environment in which to study warp propagation in the bending-wave regime, with ...the addition of an external torque due to the binary gravitational potential. In particular, we want to test the linear regime, for which an analytic theory has been developed. In order to do so, we first compute analytically the steady-state shape of an inviscid disc subject to the binary torques. The steady-state tilt is a monotonically increasing function of radius, but misalignment is found at the disc inner edge. In the absence of viscosity, the disc does not present any twist. Then, we compare the time-dependent evolution of the warped disc calculated via the known linearized equations both with the analytic solutions and with full 3D numerical simulations. The simulations have been performed with the phantom smoothed particle hydrodynamics (SPH) code using two million particles. We find a good agreement both in the tilt and in the phase evolution for small inclinations, even at very low viscosities. Moreover, we have verified that the linearized equations are able to reproduce the diffusive behaviour when α > H/R, where α is the disc viscosity parameter. Finally, we have used the 3D simulations to explore the non-linear regime. We observe a strongly non-linear behaviour, which leads to the breaking of the disc. Then, the inner disc starts precessing with its own precessional frequency. This behaviour has already been observed with numerical simulations in accretion discs around spinning black holes. The evolution of circumstellar accretion discs strongly depends on the warp evolution. Therefore, the issue explored in this paper could be of fundamental importance in order to understand the evolution of accretion discs in crowded environments, when the gravitational interaction with other stars is highly likely, and in multiple systems. Moreover, the evolution of the angular momentum of the disc will affect the history of the angular momentum of forming planets.
Abstract
We present a new algorithm, multigrain, for modelling the dynamics of an entire population of small dust grains immersed in gas, typical of conditions that are found in molecular clouds and ...protoplanetary discs. The multigrain method is more accurate than single-phase simulations because the gas experiences a backreaction from each dust phase and communicates this change to the other phases, thereby indirectly coupling the dust phases together. The multigrain method is fast, explicit and low storage, requiring only an array of dust fractions and their derivatives defined for each resolution element.
In this paper, we revisit the issue of the propagation of warps in thin and viscous accretion discs. In this regime, warps are known to propagate diffusively, with a diffusion coefficient ...approximately inversely proportional to the disc viscosity. Previous numerical investigations of this problem did not find a good agreement between the numerical results and the predictions of the analytic theories of warp propagation, both in the linear and in the non-linear case. Here, we take advantage of a new, low-memory and highly efficient smoothed particle hydrodynamics (SPH) code to run a large set of very high-resolution simulations (up to 20 million SPH particles) of warp propagation, implementing an isotropic disc viscosity in different ways, to investigate the origin of the discrepancy between the theory and the numerical results. We identify the cause of the discrepancy in an incorrect calibration of disc viscosity in previous investigations. Our new and improved analysis now shows a remarkable agreement with the analytic theory both in the linear and in the non-linear regime, in terms of warp diffusion coefficient and precession rate. It is worth noting that the resulting diffusion coefficient is inversely proportional to the disc viscosity only for small amplitude warps and small values of the disc α coefficient (α≲ 0.1). For non-linear warps, the diffusion coefficient is a function of both radius and time, and is significantly smaller than the standard value. Warped accretion discs are present in many contexts, from protostellar discs to accretion discs around supermassive black holes. In all such cases, the exact value of the warp diffusion coefficient may strongly affect the evolution of the system and therefore its careful evaluation is critical in order to correctly estimate the system dynamics.
Dusty gas with one fluid Laibe, Guillaume; Price, Daniel J.
Monthly notices of the Royal Astronomical Society,
05/2014, Volume:
440, Issue:
3
Journal Article
Peer reviewed
Open access
In this paper, we show how the two-fluid equations describing the evolution of a dust and gas mixture can be re-formulated to describe a single fluid moving with the barycentric velocity of the ...mixture. This leads to evolution equations for the total density, momentum, the differential velocity between the dust and the gas phases and either the dust-to-gas ratio or the dust fraction. The equations are similar to the usual equations of gas dynamics, providing a convenient way to extend existing codes to simulate two-fluid mixtures without modifying the code architecture. Our approach avoids the inherent difficulties related to the standard approach where the two phases are separate and coupled via a drag term. In particular, the requirements of infinite spatial and temporal resolution as the stopping time tends to zero are no longer necessary. This means that both small and large grains can be straightforwardly treated with the same method, with no need for complicated implicit schemes. Since there is only one resolution scale the method also avoids the problem of unphysical trapping of one fluid (e.g. dust) below the resolution of the other. We also derive a simplified set of equations applicable to the case of strong drag/small grains, consisting of the standard fluid equations with a modified sound speed, plus an advection-diffusion equation for the dust-to-gas ratio. This provides a simple and fast way to evolve the mixture when the stopping time is smaller than the Courant time step. We present a smoothed particle hydrodynamics implementation in a companion paper. PUBLICATION ABSTRACT
We compare the statistics of driven, supersonic turbulence at a high Mach number using flash, a widely used Eulerian grid-based code, and phantom, a Lagrangian smoothed particle hydrodynamics (SPH) ...code at resolutions of up to 5123 in both grid cells and SPH particles. We find excellent agreement between codes on the basic statistical properties: a slope of k−1.95 in the velocity power spectrum for hydrodynamic, Mach 10 turbulence, evidence in both codes for a Kolmogorov-like slope of k−5/3 in the variable ρ1/3 v as suggested by Kritsuk et al. and a lognormal probability distribution function (PDF) with a width that scales with the Mach number and proportionality constant b= 0.33 –0.5 in the density variance–Mach number relation. The measured structure function slopes are not converged in either code at 5123 elements. We find that for measuring volumetric statistics such as the power spectrum slope and structure function scaling, SPH and grid codes give roughly comparable results when the number of SPH particles is approximately equal to the number of grid cells. In particular, to accurately measure the power spectrum slope in the inertial range, in the absence of sub-grid turbulence models, requires at least 5123 computational elements in either code. On the other hand the SPH code was found to be better at resolving dense structures, giving maximum densities at a resolution of 1283 particles that were similar to the maximum densities resolved in the grid code at 5123 cells, reflected also in the high density tail of the PDF. We find SPH to be more dissipative at comparable numbers of computational elements in statistics of the velocity field, but correspondingly less dissipative than the grid code in the statistics of density-weighted quantities such as ρ1/3 v. For SPH simulations of high Mach number turbulence, we find it important to use sufficient non-linear β-viscosity in order to prevent particle interpenetration in shocks (we require βvisc= 4 instead of the widely used default value, βvisc= 2).
Abstract
Black hole—neutron star (BH–NS) mergers are a major target for ground-based gravitational wave observatories. A merger can also produce an electromagnetic counterpart (a kilonova) if it ...ejects neutron-rich matter that assembles into heavy elements through
r
-process nucleosynthesis. We study the kilonova signatures of the unbound dynamical ejecta of a BH–NS merger. We take as our initial state the results from a numerical relativity simulation and then use a general relativistic hydrodynamics code to study the evolution of the ejecta with parameterized
r
-process heating models. The unbound dynamical ejecta is initially a flattened, directed tidal tail largely confined to a plane. Heating from the
r
-process inflates the ejecta into a more spherical shape and smooths its small-scale structure, though the ejecta retains its bulk directed motion. We calculate the electromagnetic signatures using a 3D radiative transfer code and a parameterized opacity model for lanthanide-rich matter. The light curve varies with viewing angle because of two effects: asphericity results in brighter emission for orientations with larger projected areas, while Doppler boosting results in brighter emission for viewing angles more aligned with the direction of bulk motion. For typical
r
-process heating rates, the peak bolometric luminosity varies by a factor of ∼3 with orientation while the peak in the optical bands varies by ∼3 magnitudes. The spectrum is blueshifted at viewing angles along the bulk motion, which increases the
V
-band peak magnitude to ∼−14 despite the lanthanide-rich composition.
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