Difference between Enzo & Gadget astronomy simulation codes Enzo and Gadget are simulation codes used in astronomy. 
What are the largest differences between them both in terms of physics they simulate and in their implementations?
 A: Enzo is fundamentally a grid-based finite-volume hydrodynamics code. That is, the domain is divided into cells, each is assigned various fluid properties (density, velocity, etc.), and at each timestep fluxes of those quantities across the interfaces between cells are used to update the quantities in the cells. It has a choice of particular methods for accomplishing this.
Gadget is an SPH code. That means its fundamental quantities are particles rather than volumes. Particles in the code physically represent bundles of many particles in real life, and that's where the "smooth" part of SPH comes in -- when needed, the locations of the discrete particles are used to reconstruct a smooth distribution.
These are two very different methods for solving the same underlying equations. Finite-volume methods excel at conserving things like energy and momentum that ought to be conserved, and they are also very good at "shock capturing" -- not smearing out discontinuities in fluid properties when they should not be smeared out. They have difficulty adapting resolution to where it's needed (imagine a very dynamically interesting galaxy surrounded by near-vacuum -- you either miss features in the galaxy or waste time simulating the surrounding to too-high precision), but this can be overcome with adaptive mesh refinement, as it is in Enzo. SPH naturally has more particles and thus more resolution where mass has come together.
Both codes are extensively (primarily?) used for cosmological simulations. In these you have a pressureless, self-gravitating fluid (dark matter) in an expanding universe. There might be extra physics included, such as having another fluid component subject to gas pressure (normal baryonic matter), maybe with magnetic fields or radiation thrown in as well. On smaller scales (e.g. star formation) one neglects the dark matter and focuses on (self-gravitating) non-pressureless gas (with radiation and magnetic fields).
Note that in addition to finite-volume and SPH methods, there are moving-mesh and spectral methods, both of which are also used in astrophysical hydrodynamics simulations.
