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Applied Math Colloquium

Friday, February 14, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Kinetic Methods for CFD

Li-Shi Luo

Old Dominion University, Virginia, USA and Beijing Computational Science Research Center, Beijing, China

Abstract

Traditionally, computational fluid dynamics (CFD) is based on direct discretizations of the Navier-Stokes 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 -- 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 reach. 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 and the gas-kinetic scheme, their mathematical theory and their applications to simulate various complex flows. Examples include incompressible homogeneous isotropic turbulence, hypersonic flows, and micro-flows.