Showing papers by "Raul Borsche published in 2021"

Relaxation models for scalar traffic networks and zero relaxation limit

Abstract: In this paper we propose coupling conditions for a relaxation model for vehicular traffic on networks. We present a matched asymptotic expansion procedure to derive a LWR- network with well-known classical coupling conditions from the relaxation network in the macroscopic limit. Similar to the asymptotic limit of boundary value problems, we perform an asymptotic analysis of the interface layers at the nodes and a matching procedure using half-Riemann problems for the limit conservation law. Moreover, we present numerical experiments comparing the relaxation network with the LWR network for a broader range of coupling conditions.

Asymptotic Methods for Kinetic and Hyperbolic Evolution Equations on Networks

Abstract: We consider kinetic and associated macroscopic equations on networks. A general approach to derive coupling conditions for the macroscopic equations from coupling conditions of the underlying kinetic problem is presented using an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixpoint problem involving the coupled solutions of kinetic half-space problems. The procedure is explained for two simplified situations. The linear case is discussed for a linear kinetic BGK-type model leading in the macroscopic limit to a linear hyperbolic problem. The nonlinear situation is investigated for a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic conservation law on a network. Numerical comparisons between the solutions of the macroscopic equation with different coupling conditions and the kinetic solution are presented for the case of tripod and more complicated networks.