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A stochastic lattice gas for Burgers' equation: A practical study

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Abstract

We continue our investigation of stochastic lattice gases as a (highly parallel) means of simulating given PDEs, in this case Burgers' equation in one dimension. The lattice dynamics consists of stochastic unidirectional particle displacement, and our attention is turned toward the reliability of the model, i.e., its ability to reproduce the unique physical solution of Burgers' equation. Lattice gas results are discussed and compared against finite-difference calculations and exact solutions in examples which include shocks and rarefaction waves.

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Authors and Affiliations

  1. CFD/MPC Project, IMHEF Ecole Polytechnique Fédérale de Lausanne, C.P. 123, CH-1015, Lausanne, Switzerland

    Leesa Brieger & Ernesto Bonomi

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  1. Leesa Brieger
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  2. Ernesto Bonomi
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Brieger, L., Bonomi, E. A stochastic lattice gas for Burgers' equation: A practical study. J Stat Phys 69, 837–855 (1992). https://doi.org/10.1007/BF01050436

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  • DOI: https://doi.org/10.1007/BF01050436

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