A Density Independent Formulation of Smoothed Particle Hydrodynamics

The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low (high) density side is over (under) estimated. Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure), and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, point like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie & Thomas (2001) as a special case. Our formulation can be extended to handle a non-ideal gas easily.Comment: 24 pages, 21 figures. Movies and high resolution figures are available at http://v1.jmlab.jp/~saitoh/sph/index.htm

Dusty gas with SPH - II. Implicit timestepping and astrophysical drag regimes

In a companion paper (Laibe & Price 2011b), we have presented an algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the exact conservation of the both linear and angular momentum in the underlying SPH algorithm, but unlike previous schemes, allows the iterations to converge to arbitrary accuracy and is suited to the treatment of non- linear drag regimes. The algorithm presented in Paper I is also extended to deal with realistic astrophysical drag regimes, including both linear and non-linear Epstein and Stokes drag. The scheme is benchmarked against the test suite presented in Paper I, including i) the analytic solutions of the dustybox problem and ii) solutions of the dustywave, dustyshock, dustysedov and dustydisc obtained with explicit timestepping. We find that the implicit method is 1- 10 times faster than the explicit temporal integration when the ratio r between the the timestep and the drag stopping time is 1 < r < 1000.Comment: Accepted for publication in MNRA

An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows

A type of overlapping grid in spherical coordinates called the Yin-Yang grid is successfully implemented into a 3D version of the explicit Eulerian grid-based code PROMETHEUS including self-gravity. The modified code successfully passed several standard hydrodynamic tests producing results which are in very good agreement with analytic solutions. Moreover, the solutions obtained with the Yin-Yang grid exhibit no peculiar behaviour at the boundary between the two grid patches. The code has also been successfully used to model astrophysically relevant situations, namely equilibrium polytropes, a Taylor-Sedov explosion, and Rayleigh-Taylor instabilities. According to our results, the usage of the Yin-Yang grid greatly enhances the suitability and efficiency of 3D explicit Eulerian codes based on spherical polar coordinates for astrophysical flows.Comment: 15 pages, 17 figures, 2 tables, accepted for publication in A&

Kelvin-Helmholtz instabilities in Smoothed Particle Hydrodynamics

In this paper we investigate whether Smoothed Particle Hydrodynamics (SPH), equipped with artificial conductivity, is able to capture the physics of density/energy discontinuities in the case of the so-called shearing layers test, a test for examining Kelvin-Helmholtz (KH) instabilities. We can trace back each failure of SPH to show KH rolls to two causes: i) shock waves travelling in the simulation box and ii) particle clumping, or more generally, particle noise. The probable cause of shock waves is the Local Mixing Instability (LMI), previously identified in the literature. Particle noise on the other hand is a problem because it introduces a large error in the SPH momentum equation. We also investigate the role of artificial conductivity (AC). Including AC is necessary for the long-term behavior of the simulation (e.g. to get $\lambda=1/2, 1$ KH rolls). In sensitive hydrodynamical simulations great care is however needed in selecting the AC signal velocity, with the default formulation leading to too much energy diffusion. We present new signal velocities that lead to less diffusion. The effects of the shock waves and of particle disorder become less important as the time-scale of the physical problem (for the shearing layers problem: lower density contrast and higher Mach numbers) decreases. At the resolution of current galaxy formation simulations mixing is probably not important. However, mixing could become crucial for next-generation simulations.Comment: 16 pages, 23 figures, accepted for publication in MNRA

RODEO: a new method for planet-disk interaction

In this paper we describe a new method for studying the hydrodynamical problem of a planet embedded in a gaseous disk. We use a finite volume method with an approximate Riemann solver (the Roe solver), together with a special way to integrate the source terms. This new source term integration scheme sheds new light on the Coriolis instability, and we show that our method does not suffer from this instability. The first results on flow structure and gap formation are presented, as well as accretion and migration rates. For Mpl < 0.1 M_J and Mpl > 1.0 M_J (M_J = Jupiter's mass) the accretion rates do not depend sensitively on numerical parameters, and we find that within the disk's lifetime a planet can grow to 3-4 M_J. In between these two limits numerics play a major role, leading to differences of more than 50 % for different numerical parameters. Migration rates are not affected by numerics at all as long as the mass inside the Roche lobe is not considered. We can reproduce the Type I and Type II migration for low-mass and high-mass planets, respectively, and the fastest moving planet of 0.1 M_J has a migration time of only 2.0 10^4 yr.Comment: Accepted for publication in A&

Pion Interferometry for a Granular Source of Quark-Gluon Plasma Droplets

We examine the two-pion interferometry for a granular source of quark-gluon plasma droplets. The evolution of the droplets is described by relativistic hydrodynamics with an equation of state suggested by lattice gauge results. Pions are assumed to be emitted thermally from the droplets at the freeze-out configuration characterized by a freeze-out temperature $T_f$. We find that the HBT radius $R_{out}$ decreases if the initial size of the droplets decreases. On the other hand, $R_{side}$ depends on the droplet spatial distribution and is relatively independent of the droplet size. It increases with an increase in the width of the spatial distribution and the collective-expansion velocity of the droplets. As a result, the value of $R_{out}$ can lie close to $R_{side}$ for a granular quark-gluon plasma source. The granular model of the emitting source may provide an explanation to the RHIC HBT puzzle and may lead to a new insight into the dynamics of the quark-gluon plasma phase transition.Comment: 5 pages, 4 figure

Dust flow in gas disks in the presence of embedded planets

We study the dynamics of gas and dust in a protoplanetary disk in the presence of embedded planets. We investigate the conditions for dust-gap formation in terms of particle size and planetary mass. We also monitor the amount of dust that is accreted by the planet relative to the amount of gas, which is an important parameter in determining the enrichment of solids in giant planets compared to the solid content of the central star. We use a new two-fluid hydrodynamics code to solve the flow equations for both gas and dust. For the gas, we use a Godunov-type scheme with an approximate Riemann solver (the Roe solver). The dust is treated as a pressureless fluid by essentially the same numerical method as is used for the gas. We find that it only takes a planet of 0.05 Jupiter masses to open up a gap in a disk with a significant population of mm-sized particles. Dust particles larger than 150 micron participate in gap formation. We also find that the formation of the gap severely slows down dust accretion compared to that in the gas. Therefore, it is not possible to enrich a newly formed giant planet in solids, if these solids are contained in particles with sizes from 150 micron to approximately 10 cm.Comment: 13 pages, 12 figures, accepted for publication in A&

Functional properties of roselle (Hibiscus sabdariffa L.) seed and its application as bakery product

Roselle (Hibiscus sabdariffa L.) seed is a valuable food resource as it has an excellent source of dietary fibre. Therefore, this study examined the functional properties of roselle seeds. Replacement of cookie flour with roselle seed powder at levels of 0–30 % was investigated for its effect on functional and nutritional properties of cookies. Among the four formulations cookies, the most preferred by panelists was 20 % roselle seed powder cookie (F3), followed by 10 % roselle seed powder cookie (F2) and 30 % roselle seed powder cookie (F4). The least preferred formulation among all was control cookie (F1). Cookie with 20 % roselle seed powder added showed higher content of total dietary fibre (5.6 g/100 g) as compared with control cookie (0.90 g/100 g). Besides that, cookies incorporated with roselle seed powder exhibited improved antioxidant properties. Thus, roselle seed powder can be used as a dietary fibre source and developed as a functional ingredient in food products

A 3D MHD model of astrophysical flows: algorithms, tests and parallelisation

In this paper we describe a numerical method designed for modelling different kinds of astrophysical flows in three dimensions. Our method is a standard explicit finite difference method employing the local shearing-box technique. To model the features of astrophysical systems, which are usually compressible, magnetised and turbulent, it is desirable to have high spatial resolution and large domain size to model as many features as possible, on various scales, within a particular system. In addition, the time-scales involved are usually wide-ranging also requiring significant amounts of CPU time. These two limits (resolution and time-scales) enforce huge limits on computational capabilities. The model we have developed therefore uses parallel algorithms to increase the performance of standard serial methods. The aim of this paper is to report the numerical methods we use and the techniques invoked for parallelising the code. The justification of these methods is given by the extensive tests presented herein.Comment: 17 pages with 21 GIF figures. Accepted for publication in A&