  An algorithm for simulating self-gravitating cosmological astrophysical
fluids is presented. The advantages include a large dynamic range,
parallelizability, high resolution per grid element and fast execution speed.
The code is based on a finite volume flux conservative
Total-Variation-Diminishing (TVD) scheme for the shock capturing hydro, and an
iterative multigrid solver for the gravity. The grid is a time dependent field,
whose motion is described by a generalized potential flow. Approximately
constant mass per cell can be obtained, providing all the advantages of a
Lagrangian scheme. The grid deformation combined with appropriate limiting and
smoothing schemes guarantees a regular and well behaved grid geometry, where
nearest neighbor relationships remain constant. The full hydrodynamic fluid
equations are implemented in the curvilinear moving grid, allowing for
arbitrary fluid flow relative to the grid geometry. This combination retains
all the advantages of the grid based schemes including high speed per fluid
element and a rapid gravity solver.
  The current implementation is described, and empirical simulation results are
presented. Accurate execution speed calculations are given in terms of floating
point operations per time step per grid cell. This code is freely available to
the community.
