Multiscale flow simulations using particles

Flow simulations are one of the archetypal multiscale problems. Simulations of turbulent and unsteady separated flows have to resolve a multitude of interacting scales, whereas molecular phenomena determine the structure of shocks and the validity of the no-slip boundary condition. Particle simulations of continuum and molecular phenomena can be formulated by following the motion of interacting particles that carry the physical properties of the flow. In this article we review Lagrangian, multiresolution, particle methods such as vortex methods and smooth particle hydrodynamics for the simulation of continuous flows and molecular dynamics for the simulation of flows at the atomistic scale. We review hybrid molecular-continuum simulations with an emphasis on the computational aspects of the problem. We identify the common computational characteristics of particle methods and discuss their properties that enable the formulation of a systematic framework for multiscale flow simulations.