Resolution Study for Three-dimensional Supernova Simulations with the Prometheus-Vertex Code. (arXiv:1904.01699v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Melson_T/0/1/0/all/0/1">Tobias Melson</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Janka_H/0/1/0/all/0/1">H.-Thomas Janka</a> (MPI Astrophysics, Garching)
We present a carefully designed, systematic study of the angular resolution
dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics
code. Employing a simplified neutrino heating-cooling scheme in the Prometheus
hydrodynamics module allows us to sample the angular resolution between 4
degrees and 0.5 degrees. With a newly-implemented static mesh refinement (SMR)
technique on the Yin-Yang grid, the angular coordinates can be refined in
concentric shells, compensating for the diverging structure of the spherical
grid. In contrast to previous studies with Prometheus and other codes, we find
that higher angular resolution and therefore lower numerical viscosity provides
more favorable explosion conditions and faster shock expansion. We discuss the
possible reasons for the discrepant results. The overall dynamics converge at a
resolution of about 1 degree. Applying the SMR setup to marginally exploding
progenitors is disadvantageous for the shock expansion, however, because
kinetic energy of downflows is dissipated to internal energy at resolution
interfaces, leading to a loss of turbulent pressure support and a steeper
temperature gradient. We also present a way to estimate the numerical viscosity
on grounds of the measured turbulent kinetic-energy spectrum, leading to
smaller values that are more consistent with the flow behavior witnessed in the
simulations than results following calculations in previous literature.
Interestingly, the numerical Reynolds numbers (several 100 for a resolution of
one degree or better) are in the ballpark of expected neutrino-drag effects on
relevant length scales in the turbulent postshock layer. We provide a formal
derivation and quantitative assessment of the neutrino drag terms in an
Appendix.
We present a carefully designed, systematic study of the angular resolution
dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics
code. Employing a simplified neutrino heating-cooling scheme in the Prometheus
hydrodynamics module allows us to sample the angular resolution between 4
degrees and 0.5 degrees. With a newly-implemented static mesh refinement (SMR)
technique on the Yin-Yang grid, the angular coordinates can be refined in
concentric shells, compensating for the diverging structure of the spherical
grid. In contrast to previous studies with Prometheus and other codes, we find
that higher angular resolution and therefore lower numerical viscosity provides
more favorable explosion conditions and faster shock expansion. We discuss the
possible reasons for the discrepant results. The overall dynamics converge at a
resolution of about 1 degree. Applying the SMR setup to marginally exploding
progenitors is disadvantageous for the shock expansion, however, because
kinetic energy of downflows is dissipated to internal energy at resolution
interfaces, leading to a loss of turbulent pressure support and a steeper
temperature gradient. We also present a way to estimate the numerical viscosity
on grounds of the measured turbulent kinetic-energy spectrum, leading to
smaller values that are more consistent with the flow behavior witnessed in the
simulations than results following calculations in previous literature.
Interestingly, the numerical Reynolds numbers (several 100 for a resolution of
one degree or better) are in the ballpark of expected neutrino-drag effects on
relevant length scales in the turbulent postshock layer. We provide a formal
derivation and quantitative assessment of the neutrino drag terms in an
Appendix.
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