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

2021/02/18 by Stephan Gerster, Gerster, Stephan, Michaël Herty +3
Decision Sciences · Engineering · Environmental Science · #35L65 #35R60 #90B20 #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Traffic control and management #Wind and Air Flow Studies

paper · pdf · doi:10.48550/arxiv.2102.09359

openalex publication_date 2021/02/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model,\nwhich belongs to a class of second order traffic flow models described by a\nsystem of nonlinear hyperbolic equations. The stochastic quantities are\nexpanded in terms of wavelet-based series expansions. Then, they are projected\nto obtain a deterministic system for the coefficients in the truncated series.\nStochastic Galerkin formulations are presented in conservative form and for\nsmooth solutions also in the corresponding non-conservative form. This allows\nto obtain stabilization results, when the system is relaxed to a first-order\nmodel. Computational tests illustrate the theoretical results.\n

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