Thermal fluctuations play a central role in fluid dynamics at mesoscopic scales and must be incorporated into numerical schemes in a manner consistent with statistical mechanics. In this work, we develop a fluctuating lattice Boltzmann formulation based on an orthogonal central-moments-based representation. Stochastic forcing is introduced directly in the space of central moments (CMs) and consistently paired with mode-dependent relaxation, yielding a discrete kinetic model that satisfies the fluctuation-dissipation theorem exactly at the lattice level. Owing to the orthogonality of the basis, the equilibrium covariance matrix of the central moments is diagonal, and each non-conserved mode can be interpreted as an independent discrete Ornstein-Uhlenbeck process with variance fixed by equilibrium thermodynamics. The resulting formulation guarantees exact equipartition of kinetic energy at equilibrium, preserves Galilean invariance, and retains the enhanced numerical stability characteristic of CMs-based collision operators. Explicit fluctuating schemes are constructed for the D2Q9 and D3Q27 lattices. The extension to reduced-velocity discretisation is discussed too. A comprehensive set of numerical tests verifies correct thermalisation, isotropy of equilibrium statistics, and the expected scaling of velocity fluctuations with thermal energy, density, and relaxation time. In contrast to fluctuating BGK formulations, the present method remains stable and well posed in the over-relaxation regime, including in the immediate vicinity of the stability limit. These results demonstrate that CMs-based lattice Boltzmann methods provide a natural and robust framework for fluctuating hydrodynamics, in which dissipation, noise, and kinetic mode structure are consistently aligned at the discrete level.
Cross Correlators and Galilean Invariance in Fluctuating Ideal Gas Lattice Boltzmann Simulations
我们分析了Adhikari格子玻尔兹曼方法[Europhys. Lett. 71，473（2005）]，并发现只要考虑稳定系统，即使对于小波长，它也显示出与理论的极好的一致性。这与其他有限差分和旧的格子玻尔兹曼实现相反，这些实现仅在大波长的限制下显示收敛。特别是交叉关联函数消失到小于0.5%。然而，对于较大的平均速度，伽利略不变性的违反表现出自己通过类似于那些早期的实现的幅度的错误。
Istituto per le Applicazioni del Calcolo CNR（意大利国家研究委员会计算应用研究所）；Roma Tre University（罗马第三大学）；INFN ”Tor Vergata”（意大利国家核物理研究所托尔维尔加塔分部）；Department of Physics, Harvard University（哈佛大学物理系）
We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method (FLBM) for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross-section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied …
Lattice Boltzmann Methods for Navier-Stokes Equations in General Orthogonal Coordinates for Efficient Flow Simulations using Nonuniform Clustered Grids
We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle. The ratio between deterministic and stochastic rupture times, though, decreases with $θ$. Finally, we discuss the case of fluctuat…
We study the diffusivity of a small particle immersed in a square box filled with a non-ideal multicomponent fluid in the presence of thermal fluctuations. Our approach is based on the numerical integration of fluctuating lattice Boltzmann models (LBM) for multicomponent mixtures. At changing the wettability on the particle's surface, we measure the mean square displacement (MSD) and compare with the prediction of the Stokes-Einstein theory. Two main set-ups are tested, involving periodic boundary conditions and wall boundary conditions realized on the computational box. We find that full peri…
Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We develop and investigate a new rectangular central moment LBM based on non-orthogonal moment basis (referred to as RC-LBM). The equilibria to which the central moments relax under collision in this approach are obtained from matching with those corresponding to the continuous Maxwell distribution. A Chapman-Enskog analysis is performed to derive the correction …
Multiscale method based on coupled lattice-Boltzmann and Langevin-dynamics for direct simulation of nanoscale particle/polymer suspensions in complex flows
Forests play an important role in influencing the wind resource in atmospheric boundary layers and the fatigue life of wind turbines. Due to turbulence, a difficulty in the simulation of the forest effects is that flow statistical and fluctuating content should be accurately resolved using a turbulence-resolved CFD method, which requires a large amount of computing time and resources. In this paper, we demonstrate a fast but accurate simulation platform that uses a lattice Boltzmann method with large eddy simulation on Graphic Processing Units (GPU). The simulation tool is the open-source prog…
Thermodynamically Consistent Incorporation of the Langmuir Adsorption Model into Compressible Fluctuating Hydrodynamics
Korea Advanced Institute of Science and Technology（韩国科学技术院）；San Jose State University（圣何塞州立大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Merced（加州大学默塞德分校）
