Speaker: Chi-Wang Shu, Professor, Division of Applied Mathematics, Brown University, USA
Date: July 27, 2018
Time: 10:00 am
Location: Room 1032, Block B, Zhixin Building, Central Campus
Sponsor: the School of Mathematics
We discuss a recent development of a high order finite difference numerical boundary condition for solving hyperbolic Hamilton-Jacobi equations, hyperbolic conservation laws, and convection-diffusion equations on complex geometry using a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary may not be aligned with the mesh. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions coupled with traditional extrapolation or weighted essentially non-oscillatory (WENO) extrapolation for outflow boundary conditions. The schemes are shown to be high order and stable, under the standard CFL condition for the inner schemes, regardless of the distance of the first grid point to the physical boundary, that is, the “cut-cell” difficulty is overcome by this procedure. Numerical examples are provided to illustrate the good performance of our method. This is a joint work with Jinwei Fang, Ling Huang, Tingting Li, Jianfang Lu, Jianguo Ning, Sirui Tan,Francois Vilar, Cheng Wang and Mengping Zhang.
Professor Shu received his Ph.D. degree in Mathematics from the Mathematics Department of the University of California at Los Angeles with Professor Stanley Osher as his advisor in 1986. He has been with the Division of Applied Mathematics, Brown University, as Theodore B. Stowell University Professor since 2008. He has also been a Guest Professor (since 1995) and a Changjiang Lectureship Professor (2000-2002) of the Department of Mathematics of the University of Science and Technology of China. He is the Chief Editor of Mathematics of Computation of AMS, Journal of Scientific Computing of Springer, and editor of other journals features in international mathematics and applied mathematics. His main research interests includes numerical solution of Hamilton-Jacobi type equations, computational fluid dynamics and Numerical solution of equations appearing in semi-conductor device simulations with over 140 publications. In 1992 he received the NASA Public Service Group Achievement Award for the pioneering work in Computational Fluid Dynamics as part of the ICASE algorithm team. In 1995 he received the first Feng Kang Prize of Scientific Computing from the Chinese Academy of Sciences. In 2012 he was selected as one of the inaugural class of Fellows of the American Mathematical Society (AMS).
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Edited by: Zhang Xinyuan