Displaying similar documents to “Construction of fluxes at junctions for the numerical solution of traffic flow models on networks”

Godunov-like numerical fluxes for conservation laws on networks

Vacek, Lukáš, Kučera, Václav

Similarity:

We describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. Numerical experiment comparing different approaches is presented.

An efficient implementation of the semi-implicit discontinuous Galerkin method for compressible flow simulation

Dolejší, Vít

Similarity:

We deal with a numerical simulation of the inviscid compressible flow with the aid of the combination of the discontinuous Galerkin method (DGM) and backward difference formulae. We recall the mentioned numerical scheme and discuss implementation aspects of DGM, particularly a choice of basis functions and numerical quadratures for integrations. An illustrative numerical example is presented.

Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle

Lukáš Vacek, Chi-Wang Shu, Václav Kučera (2025)

Applications of Mathematics

Similarity:

We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov’s flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way...

A numerical study of non-cavitating and cavitating liquid flow around a hydrofoil

François Beux, Maria-Vittoria Salvetti, Alexey Ignatyev, Ding Li, Charles Merkle, Edoardo Sinibaldi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

The results of a workshop concerning the numerical simulation of the liquid flow around a hydrofoil in non-cavitating and cavitating conditions are presented. This workshop was part of the conference “Mathematical and Numerical aspects of Low Mach Number Flows” (2004) and was aimed to investigate the capabilities of different compressible flow solvers for the low Mach number regime and for flows in which incompressible and supersonic regions are simultaneously present. Different physical...