Saitoh R. Takayuki, Junichiro Makino
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.
View original:
http://arxiv.org/abs/1202.4277
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