  We propose a novel scheme to numerically solve scalar conservation laws on
networks without the necessity to solve Riemann problems at the junction. The
scheme is derived using the relaxation system introduced in [Jin and Xin, Comm.
Pure Appl. Math. 48(3), 235-276 (1995)] and taking the relaxation limit also at
the nodes of the network. The scheme is mass conservative and yields well
defined and easy-to-compute coupling conditions even for general networks. We
discuss higher order extension of the scheme and applications to traffic flow
and two-phase flow. In the former we compare with results obtained in
literature.
