Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006mnras.365..199m&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Volume 365, Issue 1, pp. 199-213.
Astronomy and Astrophysics
Astronomy
16
Hydrodynamics, Methods: N-Body Simulations
Scientific paper
This paper is concerned with the smoothed particle hydrodynamic (SPH) simulation of shear flow and the recent claim by Imaeda & Inutsuka that SPH has a fundamental flaw that is revealed by shear flow simulations. In order to clarify the SPH simulations, we study several representative shear flows. First, to compare against realistic exact time-dependent solutions, we simulate steady, periodic, low Mach number, inviscid shear flow in rectangular domains and the time-dependent, viscous, low Mach number evolution of both Couette flow in a rectangular domain and axisymmetric spin-down in a cylinder. These simulations are in good agreement with exact solutions. Secondly, to determine how well SPH simulates astrophysical discs, we simulate a differentially rotating, adiabatic, self-gravitating disc using as initial states variable-mass particles on a lattice, equal-mass particles on rings and on a lattice, and particles placed at random. The results show that the SPH results agree well with theory and are independent of the initial particle setup provided they are settled to equilibrium. Thirdly, we simulate a thin, two-dimensional, gaseous torus orbiting a gravitating mass and show that it is stable for at least the time integrated, and that when strongly perturbed the motion conserves circulation.
None of these systems shows the huge density fluctuations found by Imaeda & Inutsuka. The flaw in the argument of Imaeda & Inutsuka may be the way they set up the initial configurations, but this is not certain because they do not describe their initial setup in sufficient detail to allow their simulations to be repeated. The conclusions of the present paper are in agreement with those obtained recently by Price, who simulated some of the systems considered by Imaeda & Inutsuka and found that the SPH results were in good agreement with theory.
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