Takayuki R. Saitoh

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-density (high-density) side is overestimated (underestimated). 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 the 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 as a special case. Our formulation can be extended to handle a non-ideal gas easily.

A Necessary Condition for Individual Time Steps in SPH Simulations

We show that the smoothed particle hydrodynamics (SPH) method, used with individual time steps in the way described in the literature, cannot handle strong explosion problems correctly. In the individual time-step scheme, particles determine their time steps essentially from a local Courant condition. Thus they cannot respond to a strong shock, if the pre-shock timescale is too long compared to the shock timescale. This problem is not severe in SPH simulations of galaxy formation with a temperature cutoff in the cooling function at 104 K, while it is very dangerous for simulations in which the multiphase nature of the interstellar medium under 104 K is taken into account. A solution for this problem is to introduce a time-step limiter which reduces the time step of a particle if it is too long compared to the time steps of its neighbor particles. Thus this kind of time-step constraint is essential for the correct treatment of explosions in high-resolution SPH simulations with individual time steps.

THE DYNAMICS OF SPIRAL ARMS IN PURE STELLAR DISKS

It has been believed that spirals in pure stellar disks, especially the ones spontaneously formed, decay in several galactic rotations due to the increase of stellar velocity dispersions. Therefore, some cooling mechanism, for example dissipational effects of the interstellar medium, was assumed to be necessary to keep the spiral arms. Here we show that stellar disks can maintain spiral features for several tens of rotations without the help of cooling, using a series of high-resolution three-dimensional

INTERPLAY BETWEEN STELLAR SPIRALS AND THE INTERSTELLAR MEDIUM IN GALACTIC DISKS

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Dynamics of Non-steady Spiral Arms in Disk Galaxies

-body simulations of pure stellar disks. We found that if the number of particles is sufficiently large, e.g.,

Toward First-Principle Simulations of Galaxy Formation: I. How Should We Choose Star-Formation Criteria in High-Resolution Simulations of Disk Galaxies?

3\times 10^6

ENRICHMENT OF r-PROCESS ELEMENTS IN DWARF SPHEROIDAL GALAXIES IN CHEMO-DYNAMICAL EVOLUTION MODEL

, multi-arm spirals developed in an isolated disk can survive for more than 10 Gyrs. We confirmed that there is a self-regulating mechanism that maintains the amplitude of the spiral arms. Spiral arms increase Toomres

Toward First-Principle Simulations of Galaxy Formation: II. Shock-Induced Starburst at a Collision Interface during the First Encounter of Interacting Galaxies

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Natures of a clump-origin bulge: a pseudo-bulge like but old metal-rich bulge

of the disk, and the heating rate correlates with the squared amplitude of the spirals. Since the amplitude itself is limited by the value of

Flaring up of the compact cloud G2 during the close encounter with Sgr A

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