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Testing the effect of resolution on gravitational fragmentation with Lagrangian hydrodynamic schemes

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Mon. Not. Roy. Astron. Soc.504-3_3986-3995.pdf2.42 MBPDFView/Open
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Title: Testing the effect of resolution on gravitational fragmentation with Lagrangian hydrodynamic schemes
Authors: Yamamoto, Yasuyoshi Browse this author
Okamoto, Takashi Browse this author →KAKEN DB
Saitoh, Takayuki R. Browse this author
Keywords: hydrodynamics
methods: numerical
Issue Date: Jul-2021
Publisher: Oxford University Press
Journal Title: Monthly notices of the royal astronomical society
Volume: 504
Issue: 3
Start Page: 3986
End Page: 3995
Publisher DOI: 10.1093/mnras/stab1095
Abstract: To study the resolution required for simulating gravitational fragmentation with newly developed Lagrangian hydrodynamic schemes, meshless finite-volume method (MFV) and meshless finite-mass method, we have performed a number of simulations of the Jeans test and compared the results with both the expected analytical solution and results from the more standard Lagrangian approach: smoothed particle hydrodynamics (SPH). We find that the different schemes converge to the analytical solution when the diameter of a fluid element is smaller than a quarter of the Jeans wavelength, lambda(J). Among the three schemes, SPH/MFV shows the fastest/slowest convergence to the analytical solution. Unlike the well-known behaviour of Eulerian schemes, none of the Lagrangian schemes investigated displays artificial fragmentation when the perturbation wavelength, lambda, is shorter than lambda(J), even at low numerical resolution. For larger wavelengths (lambda > lambda(J)), the growth of the perturbation is delayed when it is not well resolved. Furthermore, with poor resolution, the fragmentation seen with the MFV scheme proceeds very differently compared to the converged solution. All these results suggest that, when unresolved, the ratio of the magnitude of hydrodynamic force to that of self-gravity at the sub-resolution scale is the largest/smallest in MFV/SPH, the reasons for which we have discussed in detail. These tests are repeated to investigate the effect of kernels of higher order than the fiducial cubic spline. Our results indicate that the standard deviation of the kernel is a more appropriate definition of the 'size' of a fluid element than its compact support radius.
Rights: This article has been accepted for publication in Monthly notices of the royal astronomical society ©: 2021 Yasuyoshi Yamamoto, Takashi Okamoto, Takayuki R Saitoh Published by Oxford University Press on behalf of The Royal Astronomical Society. All rights reserved.
Type: article
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 岡本 崇

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