A review of current progress in multiscale simulations for fluid flow and heat transfer problems: The frameworks, coupling techniques and future perspectives

Abstract

Many heat transfer and fluid flow problems are multiscale in nature, and the multiscale numerical methods are needed to solve the problems by considering the phenomena in all the scales. In this paper, the current progresses of the multiscale simulations for fluid flow and heat transfer problems are reviewed. Brief introductions of the numerical methods in different scales are given, which include macroscopic continuum methods, mesoscopic particle-based lattice Boltzmann, direct simulation Monte Carlo, dissipative particle dynamics and microscopic molecular dynamics. Then the classifications, frameworks and general procedures of the multiscale methods are proposed and discussed. The multiscale methods are divided into the domain decomposition scheme and hierarchical scheme. For the domain decomposition, the information exchange techniques among the numerical methods in different scales are surveyed. Special attentions are paid to the characteristics of the mesoscopic methods that facilitate the coupling. The hierarchical scheme is further divided into serial, embedded and equation-free scheme based on the knowledge about macroscopic models. The corresponding multiscale methods are reviewed and compared. In addition, the coupling of time scales is discussed for the multiple-time-scale simulations. Finally, some issues and further developments about multiscale simulations are discussed, which include the terminology, spatial and temporal scale separation, the roles of mesoscopic methods and domain decomposition, the reduced-order models and the future applications.