Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure

Progress in Lattice Boltzmann Method

We review the recent progress and successful applications of lattice Boltzmann method (LBM) to computational fluid dynamics. To clarify the important issue in the LBM simulation, this report shows the recent progress in the LBM, and summarizes both the advantages and disadvantages of the LBM. We also discuss the immersed boundary-lattice Boltzmann method (IB-LBM) that has received much attention in recent years. Due to the common feature of using the Cartesian mesh, the IB-LBM successfully calculates the rigid particle motions in a viscous fluid. We present one of key issues in the IB-LBM, and examine the applicability of the Immersed Boundary Method to the lattice kinetic scheme (LKS) for particulate flow

DEVELOPMENT OF GAS KINETIC FLUX SOLVERS AND THEIR APPLICATIONS

Ph.DDOCTOR OF PHILOSOPH

Three-Dimensional Multi-Relaxation Time (MRT) Lattice-Boltzmann Models for Multiphase Flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.Comment: Accepted for publication in the Journal of Computational Physic

A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method

A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales

Lattice Boltzmann methods for multiphase flow and phase-change heat transfer

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