A Lattice Boltzmann Method with Adaptive Mesh Refinement (AMR) for the simulation of gas-liquid flows

Two-phase flows with dynamic interfaces are ubiquitous in daily life as well as in many industrial applications. Gas bubbles and liquid droplets are typical forms of these twophase flows. In chemical engineering, understanding the dynamics of these bubbles and droplets is crucial to the design and operation of the two-phase flow reactors, ranging from microfluidic devices to large systems such as bubble columns and three-phase fluidized beds. In recent years, advanced Computational Fluid Dynamics (CFD) simulation has been increasingly used to study the multiphase flow problems. In these CFD simulations, the interactions between different phases, including the various forces on the bubbles/droplets, need to be specified using closure models, which come from either experiment correlations, or more detailed numerical simulations. Direct numerical simulation (DNS) is capable of providing such closure relations, by detailed simulation of the motion of individual bubbles/droplets in which the motion of the gas-liquid interface is directly resolved. Several types of DNS methods have been developed, and they can be largely put into three categories: the front tracking method, the front-capturing method, and the diffused interface method. The front tracking method uses Lagrangian tracking particles to form a surface mesh that represents the interface, and these particles are convected by the local flow field in each time step to update the location of the interface. The front-capturing methods include the Volume of Fluid (VOF) and the level set method, in which the interface is represented by the contour of a scalar field, which can be the volume fraction of the gas phase in the computational cell (in VOF), or the distance to the interface (in level set method). The interfaces in both the front-tracking and front capturing methods are considered “physically sharp” with zero thickness, although they are numerically smoothed to avoid the abrupt discontinuity which causes numerical problems. In contrast, the interface in the diffused interface method is physically diffused. In other words, it has a finite thickness, and the density distribution inside the interface is determined by the thermodynamic laws.