617 RWTH Publication No: 855992        2022       
TITLE Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws
AUTHORS Niklas Kolbe
ABSTRACT A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the Riemann problem at the nodes. We numerically compare the dynamics of the solution obtained by the scheme to solutions obtained using a classical coupling condition. In particular, we investigate the case of two outgoing edges in the Lighthill-Whitham-Richards model of traffic flow and in the Buckley-Leverett model of two phase flow. Moreover, we numerically study the asymptotic preserving property of the scheme by comparing it to its preliminary form before the relaxation limit in a 1-to-1 network.
KEYWORDS
DOI 10.1002/pamm.202200150
PUBLICATION Volume23, Issue1
92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
May 2023, e202200150