  We present a suite of high-resolution simulations of an isolated dwarf galaxy
using four different hydrodynamical codes: {\sc Gizmo}, {\sc Arepo}, {\sc
Gadget}, and {\sc Ramses}. All codes adopt the same physical model which
includes radiative cooling, photoelectric heating, star formation, and
supernova (SN) feedback. Individual SN explosions are directly resolved without
resorting to sub-grid models, eliminating one of the major uncertainties in
cosmological simulations. We find reasonable agreement on the time-averaged
star formation rates as well as the joint density-temperature distributions
between all codes. However, the Lagrangian codes show significantly burstier
star formation, larger supernova-driven bubbles, and stronger galactic outflows
compared to the Eulerian code. This is caused by the behavior in the dense,
collapsing gas clouds when the Jeans length becomes unresolved: gas in
Lagrangian codes collapses to much higher densities than in Eulerian codes, as
the latter is stabilized by the minimal cell size. Therefore, more of the gas
cloud is converted to stars and SNe are much more clustered in the Lagrangian
models, amplifying their dynamical impact. The differences between Lagrangian
and Eulerian codes can be reduced by adopting a higher star formation
efficiency in Eulerian codes, which significantly enhances SN clustering in the
latter. Adopting a zero SN delay time reduces burstiness in all codes,
resulting in vanishing outflows as SN clustering is suppressed.
