Lattice Boltzmann Methods for Multiscale Fluid Problems

Abstract

Complex interdisciplinary phenomena, such as drug design, crackpropagation, heterogeneous catalysis, turbulent combustion and many others, raise a growing demand of simulational methods capable of handling the simultaneous interaction of multiple space and time scales. Computational schemes aimed at such type of complex applications often involve multiple levels of physical and mathematical description, and are consequently referred to as to multiphysics methods [1–3]. The opportunity for multiphysics methods arises whenever single-level methods, say molecular dynamics and partial differential equations of continuum mechanics, expand their range of scales to the point where overlap becomes possible. In order to realize this multiphysics potential specific efforts must be directed towards the development of robust and efficient interfaces dealing with “hand-shaking” regions where the exchange of information between the different schemes takes place. Two-level schemes combing atomistic and continuum methods for crack propagation in solids or strong shock fronts in rarefied gases have made their appearance in the early 90s. More recently, threelevel schemes for crack dynamics, combining finite-element treatment of continuum mechanics far away from the crack with molecular dynamics treatment of atomic motion in the near-crack region and a quantum mechanical description of bond-snapping in the crack tip have been demonstrated.