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Asymptotic analysis of the lattice Boltzmann equation
In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the BoltzmannExpand
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Derivation of Continuum Traffic Flow Models from Microscopic Follow-the-Leader Models
TLDR
In this paper we establish a connection between a microscopic follow-the-leader model based on ordinary differential equations and a semidiscretization of a macroscopic continuum modelbased on a conservation law. Expand
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A Hierarchy of Models for Multilane Vehicular Traffic I: Modeling
TLDR
In the present paper multilane models for vehicular traffic are considered. Expand
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Network models for supply chains
A mathematical model describing supply chains on a network is introduced. In particular, conditions on each vertex of the network are specified. Finally, this leads to a system of nonlinearExpand
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Simplified P N approximations to the equations of radiative heat transfer and applications
Simplified PN (SPN) approximations to the equations of radiative heat transfer are derived for optically thick, diffusive systems, and appropriate boundary conditions are formulated. The SPNExpand
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Gas flow in pipeline networks
TLDR
We introduce a model for gas flow in pipeline networks based on the Euler equations and present numerical results for sample networks. Expand
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Coupling conditions for gas networks governed by the isothermal Euler equations
TLDR
We investigate coupling conditions for gas transport in networks where the governing equations are the isothermal Euler equations. Expand
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An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
An asymptotic-induced scheme for nonstationary transport equations with the diffusion scaling is developed. The scheme works uniformly for all ranges of mean-free paths. It is based on the asymptoticExpand
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Optimal Control for Traffic Flow Networks
We consider traffic flow models for road networks where the flow is controlled at the nodes of the network. For the analytical and numerical optimization of the control, the knowledge of the gradientExpand
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