adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

@article{Saitoh2013,

abstract={In the standard formulation of the smoothed particle hydrodynamics (SPH), it is assumed 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, which appears often in simulations of astronomical objects. 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 effective surface tension suppresses instabilities such as the Kelvin-Helmholtz and Rayleigh-Taylor instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density and thus can handle contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, and the blob tests are all very favorable to our new formulation. We conclude that our new formulation solved practically all known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation.},

archivePrefix={arXiv},

arxivId={1202.4277},

author={Saitoh, Takayuki R. and Makino, Junichiro},

title={{A density-independent formulation of smoothed particle hydrodynamics}},

volume={768},

year={2013}

}

@article{Hosono2013,

abstract={The smoothed particle hydrodynamics (SPH) method is a useful numerical tool for the study of a variety of astrophysical and planetlogical problems. However, it turned out that the standard SPH algorithm has problems in dealing with hydrodynamical instabilities. This problem is due to the assumption that the local density distribution is differentiable. In order to solve this problem, a new SPH formulation, which does not require the differentiability of the density, have been proposed. This new SPH method improved the treatment of hydrodynamical instabilities. This method, however, is applicable only to the equation of state (EOS) of the ideal gas. In this paper, we describe how to extend the new SPH method to non-ideal EOS. We present the results of various standard numerical tests for non-ideal EOS. Our new method works well for non-ideal EOS. We conclude that our new SPH can handle hydrodynamical instabilities for an arbitrary EOS and that it is an attractive alternative to the standard SPH.},

archivePrefix={arXiv},

arxivId={1307.0916},

author={Hosono, Natsuki and Saitoh, Takayuki R. and Makino, Junichiro},

doi={10.1093/pasj/65.5.108},

eprint={1307.0916},

file={:Users/josh/Downloads/pasj65-0108.pdf:pdf},

issn={0004-6264},

keywords={hydrodynamics,methods,numerical},

number={May},

pages={1--11},

title={{Density Independent Smoothed Particle Hydrodynamics for Non-Ideal Equation of State}},