We consider the hydrodynamics in curvilinear comoving coordinates and present the equations governing the motion of a fluid with viscosity (and, in part, with heat conductivity). The underlying symmetry is spherical or planar. The Lagrangian form of the equations is suitable for numerically treating such problems as stellar collapse, neutron star dynamics, nuclear firecloud expansion, head-on heavy ion collision and pellet compression as well; for such purposes a difference scheme is given too here. Entropy production due to non-equilibrium phase transition, and a simple leak-out scheme (for drain terms) are involved.