Entropy-Conserving Scheme for Modeling Nonthermal Energies in Fluid Dynamics Simulations. (arXiv:2107.14240v2 [astro-ph.GA] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Semenov_V/0/1/0/all/0/1">Vadim A. Semenov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Kravtsov_A/0/1/0/all/0/1">Andrey V. Kravtsov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Diemer_B/0/1/0/all/0/1">Benedikt Diemer</a>
We compare the performance of energy-based and entropy-conserving schemes for
modeling nonthermal energy components, such as unresolved turbulence and cosmic
rays, using idealized fluid dynamics tests and isolated galaxy simulations.
While both methods are aimed to model advection and adiabatic compression or
expansion of different energy components, the energy-based scheme numerically
solves the nonconservative equation for the energy density evolution, while the
entropy-conserving scheme uses a conservative equation for modified entropy.
Using the standard shock tube and Zel’dovich pancake tests, we show that the
energy-based scheme results in a spurious generation of nonthermal energy on
shocks, while the entropy-conserving method evolves the energy adiabatically to
machine precision. We also show that, in simulations of an isolated $L_star$
galaxy, switching between the schemes results in $approx 20-30%$ changes of
the total star formation rate and a significant difference in morphology,
particularly near the galaxy center. We also outline and test a simple method
that can be used in conjunction with the entropy-conserving scheme to model the
injection of nonthermal energies on shocks. Finally, we discuss how the
entropy-conserving scheme can be used to capture the kinetic energy dissipated
by numerical viscosity into the subgrid turbulent energy implicitly, without
explicit source terms that require calibration and can be rather uncertain. Our
results indicate that the entropy-conserving scheme is the preferred choice for
modeling nonthermal energy components, a conclusion that is equally relevant
for Eulerian and moving-mesh fluid dynamics codes.
We compare the performance of energy-based and entropy-conserving schemes for
modeling nonthermal energy components, such as unresolved turbulence and cosmic
rays, using idealized fluid dynamics tests and isolated galaxy simulations.
While both methods are aimed to model advection and adiabatic compression or
expansion of different energy components, the energy-based scheme numerically
solves the nonconservative equation for the energy density evolution, while the
entropy-conserving scheme uses a conservative equation for modified entropy.
Using the standard shock tube and Zel’dovich pancake tests, we show that the
energy-based scheme results in a spurious generation of nonthermal energy on
shocks, while the entropy-conserving method evolves the energy adiabatically to
machine precision. We also show that, in simulations of an isolated $L_star$
galaxy, switching between the schemes results in $approx 20-30%$ changes of
the total star formation rate and a significant difference in morphology,
particularly near the galaxy center. We also outline and test a simple method
that can be used in conjunction with the entropy-conserving scheme to model the
injection of nonthermal energies on shocks. Finally, we discuss how the
entropy-conserving scheme can be used to capture the kinetic energy dissipated
by numerical viscosity into the subgrid turbulent energy implicitly, without
explicit source terms that require calibration and can be rather uncertain. Our
results indicate that the entropy-conserving scheme is the preferred choice for
modeling nonthermal energy components, a conclusion that is equally relevant
for Eulerian and moving-mesh fluid dynamics codes.
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