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.

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