  This work is the first attempt to describe the multi-dimensional structure of
accreting young stars based on fully compressible time implicit
multi-dimensional hydrodynamics simulations. One major motivation is to analyse
the validity of accretion treatment used in previous 1D stellar evolution
studies. We analyse the effect of accretion on the structure of a realistic
stellar model of the young Sun. Our work is inspired by the numerical work of
Kley \& Lin (1996, ApJ, 461, 933) devoted to the structure of the boundary
layer in accretion disks. We analyse the redistribution of accreted material
with a range of values of specific entropy relative to the bulk specific
entropy of the material in the accreting object's convective envelope. A
primary goal is to understand whether and how accreted energy deposited onto a
stellar surface is redistributed in the interior. This study focusses on the
high accretion rates characteristic of FU Ori systems. We find that the highest
entropy cases produce a distinctive behaviour in the mass redistribution, rms
velocities, and enthalpy flux in the convective envelope. This change in
behaviour is characterised by the formation of a hot layer on the surface of
the accreting object, which tends to suppress convection in the envelope. We
analyse the long-term effect of such a hot buffer zone on the structure and
evolution of the accreting object with 1D stellar evolution calculations. We
study the relevance of the assumption of redistribution of accreted energy into
the stellar interior used in the literature. One conclusion is that, for a
given amount of accreted energy transferred to the accreting object, a
treatment assuming accretion energy redistribution throughout the stellar
interior could significantly overestimate the effects on the stellar structure,
in particular, on the resulting expansion.
