Systems of conservation laws with discontinuous fluxes and applications to traffic

Rosini, Massimiliano D.

doi:10.17951/a.2019.73.2.135-173

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It leads to well-posedness issues that typically require the introduction of adapted Riemann solvers, see e.g. [15,28,37,38,43,54] The continuity of the flux at the interface is a more common interfacial coupling condition. We will not treat this case here but for the sake of comparison, let us briefly discuss it first.…”

Section: Introductionmentioning

confidence: 99%

Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure

Boutin¹,

Coquel²,

LeFloch³

2021

NHM

View full text Add to dashboard Cite

In the first part of this series, an augmented PDE system was introduced in order to couple two nonlinear hyperbolic equations together. This formulation allowed the authors, based on Dafermos's self-similar viscosity method, to establish the existence of self-similar solutions to the coupled Riemann problem. We continue here this analysis in the restricted case of one-dimensional scalar equations and investigate the internal structure of the interface in order to derive a selection criterion associated with the underlying regularization mechanism and, in turn, to characterize the nonconservative interface layer. In addition, we identify a new criterion that selects doublewaved solutions that are also continuous at the interface. We conclude by providing some evidence that such solutions can be non-unique when dealing with non-convex flux-functions.

show abstract

Section: Introductionmentioning

confidence: 99%

Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure

Boutin¹,

Coquel²,

LeFloch³

2021

NHM

View full text Add to dashboard Cite

show abstract

A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows

Bürger

Diehl

Martí

et al. 2022

NHM

View full text Add to dashboard Cite

<abstract><p>A triangular system of conservation laws with discontinuous flux that models the one-dimensional flow of two disperse phases through a continuous one is formulated. The triangularity arises from the distinction between a primary and a secondary disperse phase, where the movement of the primary disperse phase does not depend on the local volume fraction of the secondary one. A particular application is the movement of aggregate bubbles and solid particles in flotation columns under feed and discharge operations. This model is formulated under the assumption of a variable cross-sectional area. A monotone numerical scheme to approximate solutions to this model is presented. The scheme is supported by three partial theoretical arguments. Firstly, it is proved that it satisfies an invariant-region property, i.e., the approximate volume fractions of the three phases, and their sum, stay between zero and one. Secondly, under the assumption of flow in a column with constant cross-sectional area it is shown that the scheme for the primary disperse phase converges to a suitably defined entropy solution. Thirdly, under the additional assumption of absence of flux discontinuities it is further demonstrated, by invoking arguments of compensated compactness, that the scheme for the secondary disperse phase converges to a weak solution of the corresponding conservation law. Numerical examples along with estimations of numerical error and convergence rates are presented for counter-current and co-current flows of the two disperse phases.</p></abstract>

show abstract

Systems of conservation laws with discontinuous fluxes and applications to traffic

Cited by 2 publications

References 8 publications

Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure

Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure

A difference scheme for a triangular system of conservation laws with discontinuous flux modeling three-phase flows

Contact Info

Product

Resources

About