On the performance of HLL, HLLC, and Rusanov solvers for hyperbolic traffic models

This paper investigates the performances of approximate Riemann solvers (ARSs) for hyperbolic traffic models from family generic second-order flow modeling. Three are selected, including HLL, HLLC, and Rusanov solvers, evaluated comprehensively against model by Zhang (2002) a variant phase-transition Colombo with continuous solution domain. The ARSs investigated using extensive numerical tests, covering all possible waves arising in different problems, shockwaves, rarefaction waves, contact waves. We first investigate ARSs’ Euler-Upwind spatiotemporal discretization scheme. results show that HLL capture solutions to problems both models. However, HLLC solver fails remain stable specific due its wave-speed mechanism which must be tailored one another. Therefore, identified as more desirable further examines various high-resolution spatial schemes coupled third-order TVD-Runge Kutta scheme temporal discretization. considered include MINMOD MUSCL schemes, cell-based upwind (CBTOU) scheme, fifth-order WENO-JS WENO-Z schemes. It is shown combinations perform differently regarding diffusions oscillations. For instance, while combination WENO-type better than other diffusions, they can lead oscillatory behavior near intermediate states even though TVD-RK used discusses implications such real-world scenarios consisting multiple bottlenecks.