  Within the theoretical framework of divergence-type theories (DTTs), we set
up a consistent nonlinear hydrodynamical description of a conformal fluid in
flat space-time. DTTs go beyond second-order (in velocity gradients) theories,
and are closed in the sense that they do not rely on adiabatic expansions. We
show that the stress-energy tensor constructed from second-order conformal
invariants is obtained from the DTT by a consistent adiabatic expansion. The
DTT satisfies the Second Law, and is causal in a set of fluid states near
equilibrium. Finally, we compare, analytically and numerically, the equations
of motion of the DTT and its truncation to second-order terms for the case of
boost invariant flow. Our numerical results indicate that the relaxation
towards ideal hydrodynamics is significantly faster in the DTT than in the
second-order theory. Not relying on a gradient expansion, our findings may be
useful in the study of early-time dynamics and in the evolution of shock-waves
in heavy-ion collisions.
