Plenary and Semi-Plenary Lectures
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| Title: |
| Multiscale Analysis and Computation of 3D Incompressible Flows |
| Lecturer: |
| Thomas Hou |
| Abstract: |
| The understanding of scale interactions for the incompressible Euler and Navier-Stokes equations has been a major challenge. Here I will present a multiscale analysis for the 3D incompressible Euler equation with multiscale initial data. We first present a multiscale analysis based on the Lagrangian formulation. By using a Lagrangian description, we can characterize the nonlinear convection of small scales exactly and turn a convection dominated transport problem into an elliptic problem for the stream function. At the end, we derive a coupled multiscale system for the flow map and the stream function, which is well-posed. Based on our understanding in the Lagrangian formulation, we derive a similar multiscale analysis using the Eulerian formulation, which is more effective for computational purpose. Our multiscale analysis reveals some interesting structures of the Reynolds stress terms and provide a theoretical guidance in developing a systematic multiscale modeling of incompressible flow. Numerical results will be presented to demonstrate the accuracy and the robustness of the multiscale method. |
 Thomas Yizhao Hou is the Charles Lee Powell professor of applied and computational mathematics at Caltech, and is one of the leading experts in computational fluid dynamics and multiscale problems. His research interests are centered around developing analytical tools and effective numerical methods for vortex dynamics, interfacial flows, and multiscale problems. He was born in Guangzhou, China, and studied at the South China University of Technology before taking his Ph.D. from UCLA. Upon obtaining his Ph.D. in 1987, he joined the Courant Institute as a postdoc and then became a faculty member in 1989. He moved to the applied math department at Caltech in 1993, and is currently the executive officer of the department of applied and computational mathematics. He was awarded the Computational and Applied Sciences Award from the US Association of Computational Mechanics in 2005, the Morningside Gold Medal in Applied Mathematics in 2004, the SIAM Wilkinson Prize in Numerical Analysis and Scientific Computing in 2001, the Francois N. Frenkiel Award from the Division of Fluid Dynamics, American Physical Society in 1998, the Feng Kang Prize in Scientific Computing in 1997, and the Sloan Foundation Research Fellowship from 1990 to 1992. He was also an invited plenary speaker at the International Congress of Industrial and Applied Mathematics in Sydney in 2003, an invited speaker of the International Congress of Mathematicians in Berlin in 1998, and has been the founding Editor-in-Chief of a SIAM interdisciplinary journal "Multiscale Modeling and Simulation" since 2002. |
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