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

TL;DR

This paper analyzes a novel relaxation-based scheme for networked conservation laws that simplifies coupling conditions without solving Riemann problems, demonstrating its effectiveness through numerical experiments on traffic and flow models.

Contribution

It introduces a relaxation approach for network coupling that avoids Riemann problem solutions and validates its performance through numerical comparisons.

Findings

The scheme accurately captures dynamics compared to classical methods.

It preserves asymptotic limits in network simulations.

Effective for traffic and two-phase flow models.

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.