Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae
In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. The ILES approach has been applied to different contexts, with varying degrees of success. It is the de-facto standard in many astrophysical simulations and in particular in studies of core-collapse supernovae (CCSN). Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. Anisotropy, in particular, could impact the dissipative properties of the flow and enhance the turbulent pressure in the radial direction, favouring the explosion. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. Our simulations employ several different methods and span a wide range of resolutions. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov k^(-5/3) scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at low resolutions, suggesting that very high "effective Reynolds number" can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, i.e., the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where high resolution ~ 512^3, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.
Additional Information© 2015 Radice et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Received: 15 April 2015; Accepted: 12 August 2015; Published: 21 August 2015. We acknowledge helpful discussions with E Abdikamalov, WD Arnett, A Burrows, R Fisher, C Meakin, P Mösta, J Murphy, M Norman, and L Roberts. This research was partially supported by the National Science Foundation under award nos. AST-1212170 and PHY-1151197 and by the Sherman Fairchild Foundation. The simulations were performed on the Caltech compute cluster Zwicky (NSF MRI-R2 award no. PHY-0960291), on the NSF XSEDE network under allocation TG-PHY100033, and on NSF/NCSA BlueWaters under NSF PRAC award no. ACI-1440083. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. The authors declare that they have no competing interests. Authors' contributions: DR ran the simulations, performed the analysis of the data and wrote the basic draft of this paper. SMC assisted with the use of the FLASH code. CDO had the original idea that started this investigation. All of the authors took part in discussions concerning the results and contributed corrections and improvements on the early draft of the manuscript. All authors read and approved the final manuscript.
Published - art_3A10.1186_2Fs40668-015-0011-0.pdf
Submitted - 1501.03169v2.pdf