  We develop a far-from-equilibrium hydrodynamic model to evolve
ultrarelativistic heavy-ion collisions in event-by-event simulations.
Anisotropic hydrodynamics is designed to better handle the strong and highly
anisotropic expansion during the early stages of the collision. The large
gradients cause conventional second-order viscous hydrodynamic approaches to
break down at early times. Anisotropic hydrodynamics evolves the large pressure
anisotropies present in the quark-gluon plasma non-perturbatively, which
prevents negative longitudinal pressures from developing even under extreme
conditions. This increased stability allows us to start anisotropic
hydrodynamics already at a very early longitudinal proper time to evolve the
pre-hydrodynamic stage. In current pre-hydrodynamic models, the equation of
state is not consistent with the QCD equation of state used in the subsequent
fluid dynamic stage. Since our approach avoids this inconsistency, we are able
to achieve a smooth transition to non-conformal viscous hydrodynamics as the
gradients decrease over time. For our first phenomenological application, we
apply our new simulation to model fluctuating Pb+Pb collisions at LHC energies
($\sqrt{s_\text{NN}} = 2.76$ TeV) and find that our preliminary calculations
for the hadronic observables are in excellent agreement with the experimental
data.
