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[PAST EVENT] Mathematics Colloquium: Li-Shi Luo, Old Dominion University
September 27, 2013
2pm - 3pm
Speaker: Li-Shi Luo,
Department of Mathematics & Statistics
Old Dominion University
Norfolk, Virginia 23529, USA
and
Beijing Computational Science Research Center
Beijing, China
Abstract: Computational fluid dynamics (CFD) is based on direct discretizations of the Navier-Stokes equations. The 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 microflows.
Department of Mathematics & Statistics
Old Dominion University
Norfolk, Virginia 23529, USA
and
Beijing Computational Science Research Center
Beijing, China
Abstract: Computational fluid dynamics (CFD) is based on direct discretizations of the Navier-Stokes equations. The 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 microflows.
Contact
Junping Shi