Langevin theory of fluctuations in the discrete Boltzmann equation

M. Gross, M. E. Cates, F. Varnik, R. Adhikari

Research output: Contribution to journalArticlepeer-review


The discrete Boltzmann equation for both the ideal and a nonideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, a fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.

Original languageEnglish
Article numberP03030
Pages (from-to)-
Number of pages34
Journal Journal of Statistical Mechanics: Theory and Experiment
Publication statusPublished - Mar 2011


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