Time-Dependent Grid for Fluid MHD Simulations in Athena++

Many phenomena in astrophysics (collapse, blast waves, jets, etc.) involve drastically changing spatial scales. This poses a challenge for models and numerical simulations. I address this issue by implementing an expanding grid formalism in the magnetohydrodynamics code Athena++. This gives every cell a generic time dependence. It can be used to define a comoving grid, an expanding grid, or a shrinking grid in any coordinate frame offered by the code. Instead of requiring unique simulations for each spatial scale involved, the expanding grid allows for a single simulation to contain the entire time evolution of the fluid.