Kinetic layers and coupling conditions for nonlinear scalar equations on networks
Provides a rigorous derivation of coupling conditions for nonlinear hyperbolic equations on networks, relevant for traffic flow and gas dynamics modeling.
The authors derive coupling conditions for macroscopic scalar nonlinear hyperbolic equations on networks from a kinetic relaxation model via asymptotic analysis, validated by numerical experiments on tripod networks.
We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the combination of kinetic half-space problems with Riemann problems at the junction. Detailed numerical comparisons between the different models show the agreement of the coupling conditions for the case of tripod networks.