Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method are now found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing certain inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynolds number and flexible surface tension. Examples of applications are provided in fuel cells and batteries, droplet collision, boiling heat transfer and evaporation, and energy storage. Finally, further developments and future prospect of the LB method are outlined for thermofluids and energy applications.3

In this paper, a three-dimensional (3D) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is presented for convection heat transfer in porous media at the representative elementary volume (REV) scale. The model is developed in the framework of the double-distribution-function (DDF) approach: an MRT-LB model of the density distribution function with the D3Q19 lattice (or D3Q15 lattice) is proposed to simulate the flow field based on the generalized non-Darcy model, while an MRT-LB model of the temperature distribution function with the D3Q7 lattice is proposed to simulate the temperature filed. The present model is employed to simulate mixed convection flow in a porous channel and natural convection in a cubical porous cavity. The numerical results demonstrate the effectiveness and accuracy of the present model in solving 3D convection heat transfer problems in porous media. The numerical results also demonstrate that the present model is approximately second-order accuracy in space. In addition, an enthalpy-based DDF-MRT model for 3D solid-liquid phase change with convection heat transfer in porous media is also presented.

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Since its introduction 30 years ago, the lattice Boltzmann (LB) method has achieved great success in simulating fluid flows and modeling physics in fluids. Owing to its kinetic nature, the LB method has the capability to incorporate the essential microscopic or mesoscopic physics, and it is particularly successful in modeling transport phenomena involving complex boundaries and interfacial dynamics.The LB method can be considered to be an efficient numerical tool for fluid flow and heat transfer in porous media. Moreover, since the LB method is inherently transient, it is especially useful for investigating transient solid-liquid phase-change processes wherein the interfacial behaviors are very important. In this article, a comprehensive review of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media at both the pore scale and representative elementary volume (REV) scale. The review first introduces the fundamentals of the LB method for fluid flow and heat transfer. Then the REV-scale LB method for fluid flow and single-phase heat transfer in porous media, and the LB method for solid-liquid phase-change heat transfer, are described. Some applications 2 of the LB methods for single-phase and solid-liquid phase-change heat transfer in porous media are provided. In addition, applications of the LB method to predict effective thermal conductivity of porous materials are also provided. Finally, further developments of the LB method in the related areas are discussed. Keyword: Lattice Boltzmann method; Single-phase heat transfer; Solid-liquid phase change; Porous media proposed the RLBE model with an enhanced collision operator, which was shown to be linearly stable. Based on the Bhatnagar-Gross-Krook (BGK) collision operator [104], the LB model using a single relaxation time, referred to as the BGK-LB model, has been independently proposed by Chen et al. [14], Koelman [15], and Qian et al. [16]. In the BGK-LB model, the equilibrium distribution function is chosen to recover the incompressible N-S equations in the incompressible limit. Due to its high efficiency and extreme simplicity, the BGK-LB model has become the most popular LB model, in spite of some well-known deficiencies (e.g., numerical instability, viscosity dependence of boundary 9 locations). Almost at the same time when the BGK-LB method was developed, d'Humières [17] proposed the multiple-relaxation-time (MRT) LB method. The MRT-LB equation (also referred to as generalized lattice Boltzmann equation (GLBE)) is an important extension of the RLBE proposed by Higuera et al. [12,13]. This work is significant because, in addition to it overcomes some deficiencies of the BGK-LB model, it facilitates the extension of the LB method, expanding the applications to a much wider range of phenomena and processes.In 1997, a direct connection between the LB equation and the continuous Boltzmann equation in kinetic theory was rigorously established by He and Luo [19,20]. In particular, it has been demonstrated that the LB equation c...

In this paper, a non-orthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) method for simulating incompressible thermal flows is presented. In the method, the incompressible Navier-Stokes