Hydrodynamics of stochastic cellular automata

A. DeMasi, R. Esposito, J. L. Lebowitz, E. Presutti

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12 Scopus citations

Abstract

We investigate a stochastic version of cellular automata used for simulating hydrodynamical flows, e.g. the HPP and FHP models. The extra stochasticity consists of "random exchanges" between neighboring cells which conserve momentum. We prove that, in suitable limits, these models satisfy the appropriate continuous Boltzmann and hydrodynamic equations, the same as those conjectured for the original models (except that there is no negative viscosity contribution). The results are obtained by proving a very strong form of propagation of chaos and by using Hilbert-Chapman-Enskog type expansions. Explicit proofs are presented for the stochastic HPP model.

Original languageEnglish (US)
Pages (from-to)127-145
Number of pages19
JournalCommunications In Mathematical Physics
Volume125
Issue number1
DOIs
StatePublished - Mar 1 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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