Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws

10/07/2022

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by   Niklas Kolbe, et al.

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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.