U.S.-China Cooperative Research: Finite Volume and Runge- Kutta Discontinuous Galerkin Methods for Conservation Laws

9601084舒该奖项支持在应用数学方面的合作，特别是在双曲型守恒律的有限体积法和龙格-库塔间断伽辽金方法方面。布朗大学应用数学教研室的舒启旺、中国科学院计算数学教研室的李银凡和合肥科技大学数学系的鲁如勋建议开展与开发高精度数值算法有关的各种项目的研究。合作将通过互访和学生交流进行。有限体积法和有限元方法是两类主要的数值方法，常用于求解流体力学以及其他计算物理和计算工程领域的微分方程，如半导体器件模拟。参与该项目的美国和中国研究人员将共同研究这两种方法，比较它们在不同情况下的相对优点，并将该方法应用于计算流体力学问题和计算物理中的其他问题。这位美国研究人员在有限差分法以及计算物理各个领域的应用方面的专业知识与中国在算法开发和分析方面的专业知识是相辅相成的。中方还为该项目带来了现有的研究小组，提供了额外的研究支持。

9601084 Shu This award supports collaboration in applied mathematics, specifically on finite volume method and Runge-Kutta discontinuous Galerkin method for hyperbolic conservation laws. Chi-Wang Shu, Brown University, Division of Applied Mathematics, and Li Yinfan, Department of Computational Mathematics, Chinese Academy of Sciences together with Lu Ruxun, Mathematics Department, University of Science and Technology, Hefei, propose to conduct research on various projects related to development of numerical algorithms with high order of accuracy. The cooperation will be carried on through exchange of visits and of students. Finite volume method and finite element method are two of the main classes of numerical methods frequently used to solve differential equations arising from fluid dynamics and other areas of computational physics and computational engineering, such as semiconductor device simulations. The US and Chinese researchers in this project will jointly study these two types of methods, compare their relative merit in different situations, and apply the method to computational fluid dynamics problems and other problems in computational physics. The US investigator's expertise in finite difference method, and in applications in various fields of computational physics is complemented by the Chinese expertise in algorithm development and analysis. The Chinese side also brings established research groups to the project, providing an additional pool of research support.