A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence

Daniel James Price, Christoph Federrath

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We compare the statistics of driven, supersonic turbulence at a high Mach number using flash, a widely used Eulerian grid-based code, and phantom, a Lagrangian smoothed particle hydrodynamics (SPH) code at resolutions of up to 5123 in both grid cells and SPH particles. We find excellent agreement between codes on the basic statistical properties: a slope of k-1.95 in the velocity power spectrum for hydrodynamic, Mach 10 turbulence, evidence in both codes for a Kolmogorov-like slope of k-5/3 in the variable 1/3 v as suggested by Kritsuk et al. and a lognormal probability distribution function (PDF) with a width that scales with the Mach number and proportionality constant b = 0.33 -0.5 in the density variance-Mach number relation. The measured structure function slopes are not converged in either code at 5123 elements.
Original languageEnglish
Pages (from-to)1659 - 1674
Number of pages16
JournalMonthly Notices of the Royal Astronomical Society
Issue number3
Publication statusPublished - 2010

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