A Godunov type scheme for a class of LWR traffic flow models with non-local flux.

Friedrich, Jan; Kolb, Oliver; Göttlich, Simone

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∞ 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.

GODUNOV method; NUMERICAL analysis; PARTIAL differential equations; SCALAR field theory; TRAFFIC flow measurement; SUPPLY chains

Networks & Heterogeneous Media, 2018, Vol 13, Issue 4, p531

1556-1801

Academic Journal

10.3934/nhm.2018024