Entropy-Conserving Scheme for Modeling Nonthermal Energies in Fluid
  Dynamics Simulations
  We compare the performance of energy-based and entropy-conservative 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 non-conservative 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.
