  Tensors describing boost-invariant and cylindrically symmetric expansion of a
relativistic dissipative fluid are decomposed in a suitable chosen basis of
projection operators. This leads to a simple set of scalar equations which
determine the fluid behavior. As special examples, we discuss the case of the
Israel-Stewart theory and the model of highly-anisotropic and
strongly-dissipative hydrodynamics ADHYDRO. We also introduce the matching
conditions between the ADHYDRO description suitable for the very early stages
of heavy-ion collisions and the Israel-Stewart theory applicable for later
stages when the system is close to equilibrium.
