Lattice Boltzmann in micro- and nano- flow simulations

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.One of the fundamental difficulties in micro- and nano-flow simulations is that the validity’s of the continuum assumption and the hydro-dynamic 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, is recently shown to converge asymptotically to the continuum Boltzmann-BGK 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 modeled 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 (CFD) and matured to the extend of commercial applications. In this talk, 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