A Density Independent Formulation of Smoothed Particle Hydrodynamics

Details A Density Independent Formulation of Smoothed Particle Hydrodynamics A Density Independent Formulation of Smoothed Particle Hydrodynamics

2012-02-20

arxiv.org/abs/1202.4277v2

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

14 pages, 13 figures, submitted to ApJ. Movies and high resolution figures are available at http://v1.jmlab.jp/~saitoh/sph/ind

Scientific paper

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.

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