We present a framework based on the generalized lattice-Boltzmann equation using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale turbulence effects are represented by the standard Smagorinsky eddy-viscosity model, which is modified by using the van Driest wall-damping function for near wall effects. For simulation of a wider class of problems, we introduce general forcing terms in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the non-equilibrium moments of the GLBE to include such forcing terms. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach is assessed for two canonical flow problems bounded by walls, viz., fully-developed turbulent channel flow at a shear or friction Reynolds number ($\mathrm{Re}$) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a $\mathrm{Re}$ of 12,000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement, with marked improvement in numerical stability characteristics.
Effect of the forcing term in the pseudopotential lattice Boltzmann modeling of thermal flows
赝势格子Boltzmann（LB）模型是LB界中用于模拟多相流的流行模型。近年来，基于赝势LB模型和双分布函数LB方法，提出了几种热LB模型来模拟热多相流[G. Házi和A. Márkus，Phys.Rev.E77，026305（2008）; L. Biferale等人，物理修订版信函108，104502（2012）; S. Gong和P. Cheng，Int. J. Heat Mass Transfer 55，4923（2012）]。本文的目的是表明，在热流的赝势LB模拟中，必须消除强迫项对温度方程的影响。首先，通过Chapman-Enskog分析显示了强迫项对温度方程的影响。为了比较，提供了不受强迫项影响的替代治疗。随后，数值研究进行了两个基准测试。数值结果清楚地表明，强迫项效应的存在将导致显着的数值误差的赝势LB模型的热流。
Three-dimensional central-moments-based lattice Boltzmann method with external forcing: A consistent, concise and universal formulation
基于级联或中心矩的格子玻尔兹曼方法（CM-LBM）是模拟高雷诺数流动的更传统的BGK-LBM的稳健替代方案。不幸的是，它的原始公式使得它很难扩展到更广泛的物理学范围。为了解决这个问题，最近的工作[A。De Rosis，Phys.Rev.E95，013310（2017）]提出了一种更通用的方法来获得简洁有效的三维CM-LBM。知道原始模型还依赖于以特定方式导出的中心矩，即，通过模仿麦克斯韦-玻尔兹曼分布，以确保其伽利略不变性后验，最近的努力[A. De Rosis和K. H. Luo，Phys. Rev. E 99，013301（2019）]进一步推广了它们的推导。后者表明，人们可以推导出伽利略不变CM在一个系统的和先验的方式，考虑高阶厄米多项式的离散平衡态的推导。结合这两种方法，提出了一个紧凑的和数学上合理的制定CM-LBM与外部强迫。更具体地说，建议的形式主义充分利用D3 Q27离散化依赖于相应的一组27埃尔米特多项式（六阶）的离散平衡态和强迫项的推导。目前的方法是更一致的比以前的方法，因为它正确地解释了如何推导出伽利略不变CM的强迫项在一个先验的方式。此外，在保持原来的CM-LBM的数值特性，目前的工作导致一个紧凑和简单的算法，代表一个普遍的方法的基础上CM和外部强迫晶格玻尔兹曼框架内。
A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part II, turbulent flows
A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part II: Extension towards turbulent flow simulation
[Geier \textit{et al.}，Phys. Rev. E \textbf{63}，066705（2006）]中提出的级联或基于中心矩的格子玻尔兹曼方法（CLBM）具有非常好的数值稳定性。然而，在三维（3D）CLBM模拟中存在两个约束。首先，传统的实现三维CLBM涉及繁琐的操作，并需要更高的计算成本相比，单弛豫时间（SRT）LBM。其次，将一般力场准确地结合到3D CLBM中是一个挑战。在本文中，我们提出了一种改进的方法来实现三维CLBM。其主要策略是采用简化的中心矩集合，并在一般的多松弛时间框架下实现基于中心矩的碰撞算子。其次，最近提出的一致强迫方案在CLBM [L。Fei和K. H. Luo，Phys. Rev. E \textbf{96}，053307（2017）]扩展为将一般力场并入3D CLBM。与最近发展的非正交CLBM [A. D. Rosis，Phys. Rev. E \textbf{95}，013310（2017）]，我们的实现被证明可以显著降低计算成本。揭示并讨论了非正交CLBM中采用离散平衡分布函数的不一致性。通过对几个典型的力驱动流的数值模拟，验证了这里开发的3D CLBM与一致的强迫方案，突出显示了非常好的性能，在精度，收敛性和一致性与非滑移规则。最后，这里开发的三维CLBM的技术可以应用于使三维MRT-LBM的实施和执行更有效。
A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part I: Numerical framework and its application to laminar flow simulation
Physics-Constrained Neural Closure for Lattice Boltzmann Large-Eddy Simulation
University of Rome “Tor Vergata”（罗马托尔维加塔大学）；Italian Institute of Technology（意大利理工学院）；Harvard University（哈佛大学）；Chalmers University of Technology（查尔姆斯理工大学）
Multiscale method based on coupled lattice-Boltzmann and Langevin-dynamics for direct simulation of nanoscale particle/polymer suspensions in complex flows
