  The equations of relativistic hydrodynamics are transformed so that steps
forward in time preserves local simultaneity. In these variables, the
space-time coordinates of neighboring points on the mesh are simultaneous
according to co-moving observers. Aside from the time step varying as a
function of the location on the mesh, the local velocity gradient and the local
density then evolve according to non-relativistic equations of motion. Analytic
solutions are found for two one-dimensional cases with constant speed of sound.
One solution has a Gaussian density profile when mapped into the new
coordinates. That solution is analyzed for the effects of longitudinal
acceleration in relativistic heavy ion collisions at RHIC, especially in
regards to two-particle correlation measurements of the longitudinal size.
