Recent experimental realizations of artificial gauge fields for cold atoms are promising for generating steady states carrying a mass current in strongly correlated systems, such as the Bose-Hubbard model. Moreover, a homogeneous condensate confined by hard-wall potentials from laser sheets has been demonstrated, which provides opportunities for probing the intrinsic transport properties of isolated quantum systems. Using the time-dependent density matrix renormalization group, we analyze the effect of the lattice and interaction strength on the current generated by a quench in the artificial vector potential when the density varies from low values (continuum limit) up to integer filling in the Mott-insulator regime. There is no observable mass current deep in the Mott-insulator state as one may expect. Other observable quantities used to characterize the quasisteady state in the bulk of the system are the Drude weight and entanglement entropy production rate. The latter in particular provides a striking signature of the superfluid-Mott-insulator transition. Furthermore, an interesting property of the superfluid state is the formation of shock and rarefaction waves at the boundaries due to the hard-wall confining potentials. We provide results for the height and the speed of the shock front that propagates from the boundary toward the center of the lattice. Our results should be verifiable with current experimental capabilities.