Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number.
Cascaded lattice Boltzmann method for incompressible thermal flows with heat sources and general thermal boundary conditions
基于级联或中心矩的格子玻尔兹曼方法（CLBM）是LBM领域中的一个相对较新的发展，与经典的单关系时间（SRT）LBM相比，它具有更好的数值稳定性，并且对于特定的格子自然地实现更好的伽利略不变性。最近，CLBM已经扩展到基于双分布函数（DDF）方法的热流模拟[L。Fei \textit{et al.}，Int. J. Heat Mass Transfer 120，624（2018）]。在这项工作中，CLBM进一步扩展到模拟涉及复杂的热边界条件和/或热源的热流。特别地，在中心矩空间中提出了一个离散的源项，以包括一个热源，并采用一般的反弹格式来实现热边界条件。对几个典型问题的数值结果与文献中的解析解和/或数值结果吻合较好，验证了CLBM在热流问题中的应用.
Central Moment Lattice Boltzmann Method using a Pressure-based Formulation for Multiphase Flows at High Density Ratios and including Effects of Surface Tension and Marangoni Stresses
[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。
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 Generative Deep Learning and Explainable Machine Learning Framework for Heat Transfer Prediction and Analysis in Porous Structures with Oscillatory Flows
Department of Mechanical and Aerospace Engineering, University of Houston（休斯顿大学机械与航空航天工程系）；Department of Mechanical Engineering, Rice University（莱斯大学机械工程系）；Department of Mechanical Engineering, Embry‑Riddle Aeronautical University（埃默里-里德尔航空大学机械工程系）
