211 research outputs found
A one-parameter family of interpolating kernels for Smoothed Particle Hydrodynamics studies
A set of interpolating functions of the type f(v)={(sin[v pi/2])/(v pi/2)}^n
is analyzed in the context of the smoothed-particle hydrodynamics (SPH)
technique. The behaviour of these kernels for several values of the parameter n
has been studied either analytically as well as numerically in connection with
several tests carried out in two dimensions. The main advantage of this kernel
relies in its flexibility because for n=3 it is similar to the standard widely
used cubic-spline, whereas for n>3 the interpolating function becomes more
centrally condensed, being well suited to track discontinuities such as shock
fronts and thermal waves.Comment: 36 pages, 12 figures (low-resolution), published in J.C.
rpSPH: a novel Smoothed Particle Hydrodynamics Algorithm
We suggest a novel discretisation of the momentum equation for Smoothed
Particle Hydrodynamics (SPH) and show that it significantly improves the
accuracy of the obtained solutions. Our new formulation which we refer to as
relative pressure SPH, rpSPH, evaluates the pressure force in respect to the
local pressure. It respects Newtons first law of motion and applies forces to
particles only when there is a net force acting upon them. This is in contrast
to standard SPH which explicitly uses Newtons third law of motion continuously
applying equal but opposite forces between particles. rpSPH does not show the
unphysical particle noise, the clumping or banding instability, unphysical
surface tension, and unphysical scattering of different mass particles found
for standard SPH. At the same time it uses fewer computational operations. and
only changes a single line in existing SPH codes. We demonstrate its
performance on isobaric uniform density distributions, uniform density shearing
flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock
tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa
Barbara galaxy cluster formation test. rpSPH is an improvement these cases. The
improvements come at the cost of giving up exact momentum conservation of the
scheme. Consequently one can also obtain unphysical solutions particularly at
low resolutions.Comment: 17 pages, 13 figures. Final version. Including section of how to
break i
Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity
This paper investigates the hydrodynamic performances of an SPH code
incorporating an artificial heat conductivity term in which the adopted signal
velocity is applicable when gravity is present. In accordance with previous
findings it is shown that the performances of SPH to describe the development
of Kelvin-Helmholtz instabilities depend strongly on the consistency of the
initial condition set-up and on the leading error in the momentum equation due
to incomplete kernel sampling. An error and stability analysis shows that the
quartic B-spline kernel (M_5) possesses very good stability properties and we
propose its use with a large neighbor number, between ~50 (2D) to ~ 100 (3D),
to improve convergence in simulation results without being affected by the
so-called clumping instability. SPH simulations of the blob test show that in
the regime of strong supersonic flows an appropriate limiting condition, which
depends on the Prandtl number, must be imposed on the artificial conductivity
SPH coefficients in order to avoid an unphysical amount of heat diffusion.
Results from hydrodynamic simulations that include self-gravity show profiles
of hydrodynamic variables that are in much better agreement with those produced
using mesh-based codes. In particular, the final levels of core entropies in
cosmological simulations of galaxy clusters are consistent with those found
using AMR codes. Finally, results of the Rayleigh-Taylor instability test
demonstrate that in the regime of very subsonic flows the code has still
several difficulties in the treatment of hydrodynamic instabilities. These
problems being intrinsically due to the way in which in standard SPH gradients
are calculated and not to the implementation of the artificial conductivity
term.Comment: 26 pages, 15 figures, accepted for publication in A&
Boosting the accuracy of SPH techniques: Newtonian and special-relativistic tests
We study the impact of different discretization choices on the accuracy of
SPH and we explore them in a large number of Newtonian and special-relativistic
benchmark tests. As a first improvement, we explore a gradient prescription
that requires the (analytical) inversion of a small matrix. For a regular
particle distribution this improves gradient accuracies by approximately ten
orders of magnitude and the SPH formulations with this gradient outperform the
standard approach in all benchmark tests. Second, we demonstrate that a simple
change of the kernel function can substantially increase the accuracy of an SPH
scheme. While the "standard" cubic spline kernel generally performs poorly, the
best overall performance is found for a high-order Wendland kernel which allows
for only very little velocity noise and enforces a very regular particle
distribution, even in highly dynamical tests. Third, we explore new SPH volume
elements that enhance the treatment of fluid instabilities and, last, but not
least, we design new dissipation triggers. They switch on near shocks and in
regions where the flow --without dissipation-- starts to become noisy. The
resulting new SPH formulation yields excellent results even in challenging
tests where standard techniques fail completely.Comment: accepted for publication in MNRA
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