Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1202.4277

A Density Independent Formulation of Smoothed Particle Hydrodynamics

Takayuki R. Saitoh·Junichiro Makino
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

astro-ph.COastro-ph.IM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Takayuki R. Saitoh, Junichiro Makino. 2013-02-26. A Density Independent Formulation of Smoothed Particle Hydrodynamics. https://doi.org/10.1088/0004-637x%2F768%2F1%2F44

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Primordial black hole clustering from spectator fields for interpreting the JWST observations

The observations by the James Webb Space Telescope (JWST) have revealed unexpectedly massive galaxy candidates at high redshifts, posing a significant challenge to the $Λ$CDM model. In this work, we investigate whether primordial black holes (PBHs) with spatial clustering, generated by a light spectator field during inflation, can accelerate early structure formation. We adopt the galaxy candidates with inferred stellar mass $10^9\,M_\odot\leq M_*^{\rm obs}\leq10^{11}\,M_\odot$ at redshift $7 \leq z \leq 10$ reported by the CEERS program as a benchmark. Two different mechanisms are considered, through which PBH clustering can influence structure formation: the PBH-induced isocurvature perturbations that enhance the matter power spectrum on linear scales, and the localized seed formation and accretion by compact PBH clusters on nonlinear scales. We find that, when adopting the cosmic microwave background (CMB) isocurvature constraint $β_{\rm iso}<0.035$ at the benchmark pivot scale $k_*=0.002\,{\rm Mpc}^{-1}$, PBH clustering can produce a cumulative stellar mass density consistent with the JWST observations while satisfying the relevant isocurvature constraint. However, the allowed enhancement of structure formation is strongly suppressed when the constraint at $k_*=0.1\,{\rm Mpc}^{-1}$ is imposed, indicating a significant dependence on the choice of the pivot scale. In contrast, the localized seed effect of compact PBH clusters is strongly constrained by the CMB isocurvature bounds, while isolated supermassive PBHs produce stellar mass densities far below those inferred from the JWST observations. Our results show that PBH clustering induced by a spectator field can substantially accelerate early structure formation, but whether it can fully account for the JWST-inferred stellar mass density depends sensitively on the pivot scale adopted for the CMB isocurvature constraint.

astro-ph.CO↗
arXiv2026

Probing memory-burdened Primordial Black Holes with global 21 cm signal

We investigate the imprints of memory-burdened primordial black holes (PBH) on the global 21 cm signal during the cosmic dawn. Recent studies reopened the possibility of a mass window of PBHs as a compelling candidate for dark matter, particularly in low-mass regimes ($M_{\text {PBH}}< 10^{15}$ g) where conventional constraints from evaporation are being revisited in light of quantum gravitational effects. One such effect, the \textit{memory burden effect}, slows down black hole evaporation by incorporating the backreaction of radiation on the black hole microstates, substantially extending the lifetime of light PBHs and thus modifying their late-time emission spectra. This prolonged emission can dramatically alter the energy injection history in the early universe. By computing the modified energy injection rates into the intergalactic medium and incorporating them into the thermal and ionization evolution of neutral hydrogen, we obtain projected constraints on the fraction of dark matter. The bounds are obtained from the fact that these low mass PBHs, which were thought otherwise evaporated, can modify the absorption amplitude in the global 21-cm signal at redshift $z\approx17$. Considering the two viable scenarios of transition to the memory-burden phase: fast (or instantaneous) and slow (transition with a finite width), we show how the 21 cm bounds are sensitive to different mass ranges. For a broad transition with $δ=10^{-2}$ we find that PBHs in the mass range $M_{\rm PBH}\simeq10^{8}$-$10^{13}$g are excluded at the level of $f_{\rm PBH}\gtrsim10^{-8}$. In contrast, for a fast-transition case with the lowest suppression exponent $k=1$, the evaporation is suppressed so efficiently that no meaningful 21\,cm constraint remains for $M_{\rm PBH}\gtrsim10^{7}$g.

astro-ph.CO↗
arXiv2026

Axion Inflation with a Massive Abelian Gauge Field

An axial coupling between an inflaton and an Abelian gauge field can trigger the tachyonic amplification of one gauge-field helicity. For a massless vector, modes with physical momentum $k/a\sim |ξ|H$ are enhanced by approximately $\exp(π|ξ|)$, and sufficiently efficient production can provide substantial friction for the homogeneous inflaton. We extend this mechanism to a vector of mass $m$. The instability is present only for $|ξ|>\bar m\equiv m/H$, and in the heavy regime the mode amplitude scales as $\exp[π(|ξ|-\bar m)]$. Because the amplified modes remain well inside the Hubble radius when $\bar m\gg1$, their contribution to long-wavelength curvature perturbations $ζ$ is power-law suppressed at fixed background backreaction. In the weak-backreaction regime we obtain a spectrum ${\cal P}^{\rm id}_ζ \propto \bar m^{-w}$, with $w \sim 2$, while including the gauge-induced friction of scalar perturbations gives the scaling ${\cal P}^{\rm id}_ζ\propto \bar{m}^{-s}$, with $s$ between three and four. These estimates indicate that ${\cal P}^{\rm id}_ζ\lesssim 10^{-9}$ on CMB scales should be compatible with gauge field backreaction for $\bar{m}$ larger than order a few hundred. We test the analytical mode functions and backreaction estimates with the first lattice simulations based on a massive-vector extension of the \texttt{Pencil Code}, including simulations in the strongly backreacting regime.

astro-ph.CO↗