  We apply a novel adaptive mesh refinement code, AMRVAC, to numerically
investigate the various evolutionary phases in the interaction of a
relativistic shell with its surrounding cold Interstellar Medium (ISM). We do
this for both 1D isotropic as well as full 2D jetlike fireball models. This is
relevant for Gamma Ray Bursts, and we demonstrate that, thanks to the AMR
strategy, we resolve the internal structure of the shocked shell-ISM matter,
which will leave its imprint on the GRB afterglow. We determine the
deceleration from an initial Lorentz factor $\gamma=100$ up to the almost
Newtonian $\gamma\sim{\cal O}(2)$ phase of the flow. We present axisymmetric 2D
shell evolutions, with the 2D extent characterized by their initial opening
angle. In such jetlike GRB models, we discuss the differences with the 1D
isotropic GRB equivalents. These are mainly due to thermally induced sideways
expansions of both the shocked shell and shocked ISM regions. We found that the
propagating 2D ultrarelativistic shell does not accrete all the surrounding
medium located within its initial opening angle. Part of this ISM matter gets
pushed away laterally and forms a wide bow-shock configuration with swirling
flow patterns trailing the thin shell. The resulting shell deceleration is
quite different from that found in isotropic GRB models. As long as the lateral
shell expansion is merely due to ballistic spreading of the shell, isotropic
and 2D models agree perfectly. As thermally induced expansions eventually lead
to significantly higher lateral speeds, the 2D shell interacts with comparably
more ISM matter and decelerates earlier than its isotropic counterpart.
