Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation
We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are proje...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2021220?viewType=HTML |
| _version_ | 1819003000491868160 |
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| author | Stephan Gerster Michael Herty Elisa Iacomini |
| author_facet | Stephan Gerster Michael Herty Elisa Iacomini |
| author_sort | Stephan Gerster |
| collection | DOAJ |
| description | We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results. |
| first_indexed | 2024-12-20T23:14:03Z |
| format | Article |
| id | doaj.art-f5799cc1fc1c4d8db90210e694429794 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-20T23:14:03Z |
| publishDate | 2021-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-f5799cc1fc1c4d8db90210e6944297942022-12-21T19:23:41ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-05-011844372438910.3934/mbe.2021220Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxationStephan Gerster 0Michael Herty1Elisa Iacomini2RWTH Aachen University, Institute for Geometry and Applied Mathematics, Aachen, GermanyRWTH Aachen University, Institute for Geometry and Applied Mathematics, Aachen, GermanyRWTH Aachen University, Institute for Geometry and Applied Mathematics, Aachen, GermanyWe investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2021220?viewType=HTMLtraffic flowuncertainty quantificationstability analysisaw-rascle-zhang modelstochastic galerkinchapman-enskog expansion |
| spellingShingle | Stephan Gerster Michael Herty Elisa Iacomini Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation Mathematical Biosciences and Engineering traffic flow uncertainty quantification stability analysis aw-rascle-zhang model stochastic galerkin chapman-enskog expansion |
| title | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| title_full | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| title_fullStr | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| title_full_unstemmed | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| title_short | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| title_sort | stability analysis of a hyperbolic stochastic galerkin formulation for the aw rascle zhang model with relaxation |
| topic | traffic flow uncertainty quantification stability analysis aw-rascle-zhang model stochastic galerkin chapman-enskog expansion |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2021220?viewType=HTML |
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