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We test four commonly used astrophysical simulation codes; Enzo, Flash, Gadget and Hydra, using a suite of numerical problems with analytic initial and final states. Situations similar to the conditions of these tests, a Sod shock, a Sedov blast and both a static and translating King sphere occur commonly in astrophysics, where the accurate treatment of shocks, sound waves, supernovae explosions and collapsed haloes is a key condition for obtaining reliable validated simulations. We demonstrate that comparable results can be obtained for Lagrangian and Eulerian codes by requiring that approximately one particle exists per grid cell in the region of interest. We conclude that adaptive Eulerian codes, with their ability to place refinements in regions of rapidly changing density, are well suited to problems where physical processes are related to such changes. Lagrangian methods, on the other hand, are well suited to problems where large density contrasts occur and the physics is related to the local density itself rather than the local density gradient.
Tasker et al. (Fri,) studied this question.