The Riemann Problem with Delta Initial Data for the Non-Isentropic Improved Aw-Rascle-Zhang Model

Jiang, Weifeng; Chen, Tingting; Li, Tong; Wang, Zhen

doi:10.1007/s10473-023-0114-7

Cited by 2 publications

(1 citation statement)

References 35 publications

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“…Further developments include the solution to hyperbolic conservation laws with non-conservative terms such as ( shallow water models, horizontal temperature gradient, and pressure gradient terms, etc see in [2,23,29]. A large number of contributions has been made in this context such as the incorporation of the entropy equation for pressure gradient models by Mahmood, [24], establishing important analysis related to the existence and uniqueness of the Riemann problem for one-dimensional isentropic and non-isentropic gas dynamic equation [6,14], the modified Riemann solutions for MHD problems including magnetic field effects on elementary waves presented in [32], investigating Riemann solutions for radiating non-ideal flows [25] etc.…”

Section: Introductionmentioning

confidence: 99%

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Ahmed

2024

VFAST trans. math.

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The Rienamm solution of the Cargo-LeRoux model has been recently introduced in [1] in which authors have found the exact solutions to the initial value problem. This work is the first attempt to apply numerical methods for the Cargo-LeRoux model. The higher-order flux limiter method applied in this paper holds the total variation diminishing property and gives smooth solutions in steep gradient regions. Various limiter functions that lead to different accuracy in numerical results are tested for the Riemann problem. The numerical investigations presented in this work can be used to review limiter-based TVD schemes extensively and to construct a class of highly efficient finite volume/ finite difference methods for such models.

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Section: Introductionmentioning

confidence: 99%

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Ahmed

2024

VFAST trans. math.

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Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation

Zhang

Fan

2023

Journal of Mathematical Physics

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The Riemann problem for the Aw-Rascle (AR) traffic flow model with a double parameter perturbation containing flux and generalized Chaplygin gas is first solved. Then, we show that the delta-shock solution of the perturbed AR model converges to that of the original AR model as the flux perturbation vanishes alone. Particularly, it is proved that as the flux perturbation and pressure decrease, the classical solution of the perturbed system involving a shock wave and a contact discontinuity will first converge to a critical delta shock wave of the perturbed system itself and only later to the delta-shock solution of the pressureless gas dynamics (PGD) model. This formation mechanism is interesting and innovative in the study of the AR model. By contrast, any solution containing a rarefaction wave and a contact discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some representatively numerical results consistent with the theoretical analysis are presented.

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The Riemann Problem with Delta Initial Data for the Non-Isentropic Improved Aw-Rascle-Zhang Model

Cited by 2 publications

References 35 publications

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

Limits of solutions to the Aw-Rascle traffic flow model with generalized Chaplygin gas by flux approximation

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