Abstract
AbstractIn 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 $k^{-5/3}$ 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 ∼5123, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.
Highlights
Despite decades of studies and compelling evidence that a significant fraction (Clausen et al ) of stars with initial masses in excess of ∼ solar masses explode as core-collapse supernovae (CCSN) at the end of their evolution, the exact details of the explosion mechanism are still uncertain (Woosley and Janka ; Janka et al ; Burrows ; Foglizzo et al )
In accordance with the implicit large eddy simulation (ILES), paradigm, we do not include any additional sub-grid scale model, but relied on the implicit turbulent closure built in the numerical schemes we use for the integration of the hydrodynamics equation
We remark that the use of the artificial viscosity for PPM is not really necessary in this regime (Porter and Woodward ), our goal is not to perform a study of the turbulent dynamics, but to assess how each numerical method performs when used under the same condition as in a real CCSN simulation where strong shocks need to be handled in some parts of the domain
Summary
Despite decades of studies and compelling evidence that a significant fraction (Clausen et al ) of stars with initial masses in excess of ∼ solar masses explode as core-collapse supernovae (CCSN) at the end of their evolution, the exact details of the explosion mechanism are still uncertain (Woosley and Janka ; Janka et al ; Burrows ; Foglizzo et al ). Given the very large Reynolds numbers, as large as ∼ in the region of interest (Abdikamalov et al ) (the so-called gain region, where neutrino heating dominates over neutrino cooling), it is expected that the resulting flow will be fully turbulent It has been suggested (Murphy et al ; Couch and Ott ) recently that turbulence and, in particular, turbulent pressure could tip the balance of the forces in favor of explosion. In this respect, anisotropy is of key importance, because it results in an effective radial pressure support with adiabatic index γturb = , much larger than that of thermal (radiation) pressure (γth / ). This means that turbulent kinetic energy is a much more valuable source of radial pressure support than thermal energy (see Appendix)
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