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arXiv · 2102.09359

Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation

Stephan Gerster·Michael Herty·Elisa Iacomini
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Abstract

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.

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Stephan Gerster, Michael Herty, Elisa Iacomini. 2021-02-18. Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation. https://arxiv.org/abs/2102.09359

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