Lattice Boltzmann Equation: Failure or Success?

Abstract

The lattice Boltzmann equation (LBE) is a microscopically-inspired method designed to solve macroscopic fluid dynamics problems. As a such, it lives at the interface between the microscopic (molecular) and macroscopic (continuum) worlds, hopefully capturing the best of the two. In this paper we shall discuss whether or not, after almost a decade since its inception, LBE has lived up to the initial expectations. Open problems and future research developments are also briefly outlined.