Bound-Preserving High Order Schemes for Convection-Dominated Problems
Speaker
Prof. Chi-Wang Shu
Division of Applied Mathematics, Brown University, USA
Abstract

We give a survey of our recent work with collaborators on the construction of uniformly high order accurate discontinuous Galerkin (DG) and weighted essentially non-oscillatory (WENO) finite volume (FV) and finite difference (FD) schemes which satisfy strict maximum principle for nonlinear scalar conservation laws, passive convection in incompressible flows, and nonlinear scalar convection-diffusion equations, and preserve positivity for density and pressure for compressible Euler systems. A general framework (for arbitrary order of accuracy) is established to construct a simple scaling limiter for the DG or FV method involving only evaluations of the polynomial solution at certain quadrature points. The bound preserving property is guaranteed for the first order Euler forward time discretization or strong stability preserving (SSP) high order time discretizations under suitable CFL condition. One remarkable property of this approach is that it is straightforward to extend the method to two and higher dimensions on arbitrary triangulations. We will emphasize recent developments including high order bound-preserving schemes for relativistic hydrodynamics, high order discontinuous Galerkin Lagrangian schemes, and high order discontinuous Galerkin methods for radiative transfer equations. Numerical tests demonstrating the good performance of the scheme will be reported.

About the Speaker

舒其望, 教授, 1982年在中国科学技术大学数学系毕业取得学士学位, 1986年在美国加州大学洛杉矶分校数学系取得博士学位。1987年至1992年在美国布朗大学应用数学系担任助理教授和副教授, 1996年起在美国布朗大学应用数学系担任教授, 1999年至2005年任美国布朗大学应用数学系主任, 2008年起担任美国布朗大学Theodore B. Stowell应用数学讲座教授。他是我国第一批 "教育部长江学者讲座教授" (1998年中国科技大学)。他曾担任计算数学领域国际著名期刊 Mathematics of Computation 执行主编, 现任 Journal of Scientific Computing 主编, 并担任多个国际学术期刊的编委。曾获得美国NASA科研奖 (1992年)、首届冯康科学计算奖(1995年) 和SIAM/ACM计算科学与工程奖 (2007年)。2009年舒其望教授当选为首届美国工业与数学应用协会会士。舒其望教授主要的研究领域是计算流体力学、半导体设备模拟、宇宙天体学中出现的双曲型问题和对流占优问题的高阶数值方法的设计、分析与应用。他在科学计算领域的重要贡献包括TVD时间离散、ENO和WENO差分离散、间断Galerkin有限元方法和谱方法等。他的大量开拓性工作在计算数学、科学计算和应用领域产生了深远的影响, 他的研究工作被国内外同行多次引用。2004年起被ISI列为数学科学高引用率作者。

 

Date&Time
2016-07-15 10:00 AM
Location
Room: A203 Meeting Room
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