  This paper describes algorithms for non-relativistic hydrodynamics in the
toolkit for high-order neutrino radiation hydrodynamics (thornado), which is
being developed for multiphysics simulations of core-collapse supernovae
(CCSNe) and related problems with Runge-Kutta discontinuous Galerkin (RKDG)
methods. More specifically, thornado employs a spectral type nodal collocation
approximation, and we have extended limiters - a slope limiter to prevent
non-physical oscillations and a bound-enforcing limiter to prevent non-physical
states - from the standard RKDG framework to be able to accommodate a tabulated
nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms
with a nuclear EoS, we first present numerical results from basic test problems
in idealized settings in one and two spatial dimensions, employing Cartesian,
spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to
the problem of adiabatic collapse, shock formation, and shock propagation in
spherical symmetry, initiated with a 15 solar mass progenitor. We find that the
extended limiters improve the fidelity and robustness of the RKDG method in
idealized settings. The bound-enforcing limiter improves robustness of the RKDG
method in the adiabatic collapse application, while we find that slope limiting
in characteristic fields is vulnerable to structures in the EoS - more
specifically, in the phase transition from nuclei and nucleons to bulk nuclear
matter. The success of these applications marks an important step toward
applying RKDG methods to more realistic CCSN simulations with thornado in the
future.
