Lattice Boltzmann in micro- and nano-flow simulations

摘要

One of the fundamental difficulties in micro- and nano-flow simulations is that the validity of the continuum assumption and the hydrodynamic equations start to become questionable in this flow regime. The lower-level kinetic/molecular alternatives are often either prohibitively expensive for practical purposes or poorly justified from a fundamental perspective. The lattice Boltzmann (LB) method, which originated from a simplistic Boolean kinetic model, has recently been shown to converge asymptotically to the continuum Boltzmann-Bhatnagar-Gross-Krook equation and therefore offers a theoretically sound and computationally effective approach for micro- and nano-flow simulations. In addition, its kinetic nature allows certain microscopic physics to be modelled at the macroscopic level, leading to a highly efficient model for multiphase flows with phase transitions. With the inherent computational advantages of a lattice model, e.g., the algorithm simplicity and parallelizability, the ease of handling complex geometry and so on, the LB method has found many applications in various areas of computational fluid dynamics and matured to the extent of commercial applications. In this article, I shall give an introduction to the LB method with the emphasis given to the theoretical justifications for its applications in micro- and nano-flow simulations. Some recent examples will also be reported.