In this paper, we describe a new hydrodynamics code for 1D and 2D
astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary,
unstructured grids. The core of the hydrodynamics algorithm is an arbitrary
Lagrangian-Eulerian (ALE) approach, in which the gradient and divergence
operators are made compatible using the support-operator method. We present 1D
and 2D gravity solvers that are finite differenced using the support-operator
technique, and the resulting system of linear equations are solved using the
tridiagonal method for 1D simulations and an iterative multigrid-preconditioned
conjugate-gradient method for 2D simulations. Rotational terms are included for
2D calculations using cylindrical coordinates. We document an incompatibility
between a subcell pressure algorithm to suppress hourglass motions and the
subcell remapping algorithm and present a modified subcell pressure scheme that
avoids this problem. Strengths of this code include a straightforward
structure, enabling simple inclusion of additional physics packages, the
ability to use a general equation of state, and most importantly, the ability
to solve self-gravitating hydrodynamic flows on time-dependent, arbitrary
grids. In what follows, we describe in detail the numerical techniques employed
and, with a large suite of tests, demonstrate that BETHE-hydro finds accurate
solutions with 2nd-order convergence.Comment: 51 pages in emulateapj, including 25 figures, replace with version
accepted to ApJS, corrected typos and included minor referee's comment