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From particles to precision. Simulating subsonic turbulence with Smoothed Particle Hydrodynamics

Rubén M. Cabezón, Domingo García-Senz, Oliver Avril, Osman Seckin Simsek, Sebastian Keller, Axel S. Lechuga, Lucio Mayer, Ralf Klessen, Florina M. Ciorba

Abstract

Direct numerical simulation of subsonic turbulence with smoothed particle hydrodynamics (SPH) has traditionally been hampered by zeroth-order (E0) errors, inaccurate gradient evaluations, and excessive numerical dissipation. We demonstrate that the recently developed SPH-EXA code can overcome these challenges, producing results similar to those of other state-of-the-art non-SPH codes, such as AREPO and GIZMO. We show that SPH-EXA accurately reproduces the Kolmogorov inertial range scaling in the subsonic regime with increasing resolution, closely matching state-of-the-art non-SPH methods. This is an outstanding result given the important role of SPH codes in astrophysics and cosmology, and the ubiquity of turbulent phenomena.

From particles to precision. Simulating subsonic turbulence with Smoothed Particle Hydrodynamics

Abstract

Direct numerical simulation of subsonic turbulence with smoothed particle hydrodynamics (SPH) has traditionally been hampered by zeroth-order (E0) errors, inaccurate gradient evaluations, and excessive numerical dissipation. We demonstrate that the recently developed SPH-EXA code can overcome these challenges, producing results similar to those of other state-of-the-art non-SPH codes, such as AREPO and GIZMO. We show that SPH-EXA accurately reproduces the Kolmogorov inertial range scaling in the subsonic regime with increasing resolution, closely matching state-of-the-art non-SPH methods. This is an outstanding result given the important role of SPH codes in astrophysics and cosmology, and the ubiquity of turbulent phenomena.

Paper Structure

This paper contains 15 sections, 26 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Initial conditions
  3. Results
  4. Impact of solver elements at fixed resolution
  5. Resolution scaling and flow morphology
  6. Cross-code comparison
  7. Summary and conclusions
  8. SPH Ingredients
  9. Gradients
  10. Dissipation
  11. Volume elements
  12. SPH-EXA hydrodynamic equations
  13. The relevance of accurate grad-h terms
  14. Second-order velocity structure function
  15. High-resolution view of the velocity field

Figures (11)

  • Figure 1: Comparison of the power spectra of the velocity field with different elements incorporated into the SPH solver. The dashed line is the theoretical Kolmogorov power spectrum of $\sim k^{-5/3}$. STD denotes standard SPH and is taken from bauer_subsonic_2012. All other simulations were performed with SPH-EXA and $250^3$ particles. The meaning of the remaining acronyms is provided in Sect. \ref{['sec:results']}.
  • Figure 2: Comparison of the instantaneous power spectra of the velocity field at $t=10$ at increasing resolution. Each line corresponds to an increase of a factor of 2 in resolution with respect to the previous curve.
  • Figure 3: Slice of thickness $2h$ centered on $z=0$ showing the velocity magnitude with increasing resolution (SPH-EXA). We represent particles directly.
  • Figure 4: Instantaneous density PDF for the $400^3$ simulation at $t=10$. Comparison of mass-weighted and volume-weighted PDFs.
  • Figure 5: Comparison of the velocity power spectra for different codes at $t=10$. AREPO and GIZMO curves are from their respective papers.
  • ...and 6 more figures