I n the quest to model complex physical phenomena, overstating the need for simu- lational tools that can handle multiple space and time scales is hard. The capability of addressing problems across several length and time scales is a hallmark of modern computa- tional science, the goal of which is to tackle is- sues that straddle various traditional disciplines of science and engineering. Some interesting ex- amples of such phenomena that have received considerable attention recently are drug design, the brittle or ductile failure of structural mate- rials, heterogeneous catalysis, and turbulent combustion. We have come to know computa- tional schemes aimed at such complex applica- tions that involve multiple levels of physical and mathematical descriptions as multiscale methods. One approach to multiscale modeling meth- ods is to integrate schemes, which usually apply to a single-scale regime. This approach’s central issue is dealing with the “hand-shaking” regions: At these regions, the different schemes that han- dle individual scales need to exchange informa- tion in a way that is physically meaningful, math- ematically consistent, and computationally efficient. Two-level schemes combing atomistic and continuum methods for crack propagation in solids, or strong shock fronts in rarefied gases, made their appearance in the early 1990s. 1–3 More recently, researchers have applied three- level schemes to study crack dynamics, combin- ing a finite-element (FE) treatment of contin- uum mechanics in regions far from the crack, a molecular dynamics (MD) treatment of atomic motion near the crack, and a quantum mechan- ical (QM) description of bonding in the crack tip’s immediate neighborhood. 4 This FE-MD- QM implementation represents a concrete ex- ample of composite algorithms—that is, meth- ods that involve seamless interfaces between the different mathematical models associated with different physical levels of description. An alternative approach is to explore methods that can host more than one physical level of de- scription—for example, atomistic, kinetic, and fluid—within the same mathematical frame- work. A potential candidate is the Lattice Boltz- mann equation method. The LBE is a minimal form of the Boltzmann kinetic equation in 26 COMPUTING IN SCIENCE & ENGINEERING A PPLYING THE L ATTICE B OLTZMANN E QUATION TO MULTISCALE F LUID P ROBLEMS The authors discuss the theory and application of the Lattice Boltzmann equation to multiscale physics in fluids. They present two examples relevant to real-life applications: airflow around an airfoil at high Reynolds numbers and reactive flow in micropores. M ATERIALS S CIENCE SAURO SUCCI National Research Council, Italy OLGA FILIPPOVA Duisburg University, Germany GREG SMITH AND EFTHIMIOS KAXIRAS Harvard University 1521-9615/01/$10.00 © 2001 IEEE