  We present a Godunov type numerical scheme for a class of scalar conservation
laws with non-local flux arising for example in traffic flow models. The
proposed scheme delivers more accurate solutions than the widely used
Lax-Friedrichs type scheme. In contrast to other approaches, we consider a
non-local mean velocity instead of a mean density and provide $L^\infty$ and
bounded variation estimates for the sequence of approximate solutions. Together
with a discrete entropy inequality, we also show the well-posedness of the
considered class of scalar conservation laws. The better accuracy of the
Godunov type scheme in comparison to Lax-Friedrichs is proved by a variety of
numerical examples.
