Belardinelli D, Sbragaglia M, Biferale L, Gross M, Varnik F
Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy.
Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):023313. doi: 10.1103/PhysRevE.91.023313. Epub 2015 Feb 24.
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
波动格子玻尔兹曼方程（FLBEs）的当前实现描述的是单组分流体。在本文中，一个基于连续介质动力学玻尔兹曼方程来描述多组分流体的模型被扩展，以纳入热涨落的影响。由此得到的波动玻尔兹曼方程首先被线性化，以便应用线性涨落理论，并且通过直接在动力学层面调用涨落耗散定理来确定噪声协方差的表达式。对我们的分析至关重要的是将玻尔兹曼方程投影到正交厄米特基上。通过在空间和时间上对具有离散速度数目的波动玻尔兹曼方程进行积分，得到了理想和非理想多组分流体的FLBE。数值模拟专门针对在晶格上引入平均场相互作用的情况，表明系统有适当的热化。
