Kinetic Methods for CFD - A Multiscale Approach

Abstract: Traditionally, fluid flow is modeled by macroscopic hydrodynamic equations, i.e., the Euler or the Navier-Stokes equations. Naturally, computational fluid dynamics (CFD) is based on direct discretizations of the hydrodynamic equations.  This traditional approach of CFD is now being challenged as new multi-scale and multi-physics problems have begun to emerge in many fields, because in nanoscale systems, the scale separation assumption does not hold; macroscopic theory is therefore inadequate, yet microscopic theory may be impractical because it requires computational capabilities far beyond our present each.  Methods based on mesoscopic theories, which connect the microscopic and macroscopic descriptions of the dynamics, provide a promising approach.  Besides their connection to microscopic physics, kinetic methods also have certain numerical advantages due to the linearity of the advection term in the Boltzmann equation.  We will discuss two mesoscopic methods: the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS), their mathematical theory and their applications to simulate various complex and/or nonequilibrium flows. Examples include incompressible homogeneous isotropic turbulence, hypersonic flows, and micro-flows.