  We present a new numerical framework to model the formation and evolution of
giant planets. The code is based on the further development of the stellar
evolution toolkit Modules for Experiments in Stellar Astrophysics (MESA). The
model includes the dissolution of the accreted planetesimals/pebbles, which are
assumed to be made of water ice, in the planetary gaseous envelope, and the
effect of envelope enrichment on the planetary growth and internal structure is
computed self-consistently. We apply our simulations to Jupiter and investigate
the impact of different heavy-element and gas accretion rates on its formation
history. We show that the assumed runaway gas accretion rate significantly
affect the planetary radius and luminosity. It is confirmed that heavy-element
enrichment leads to shorter formation timescales due to more efficient gas
accretion. We find that with heavy-element enrichment Jupiter's formation
timescale is compatible with typical disks' lifetimes even when assuming a low
heavy-element accretion rate (oligarchic regime). Finally, we provide an
approximation for the heavy-element profile in the innermost part of the
planet, providing a link between the internal structure and the planetary
growth history.
