报告题目：Hermite WENO schemes for hyperbolic conservation laws

主讲人：邱建贤

时 间：2023年9月4日16:00

地 点：理学院会议室306

主讲人简介：

  邱建贤，厦门大学数学科学学院教授，国际著名刊物 “J. Comp. Phys.” (计算物理) 编委。从事计算流体力学及微分方程数值解法的研究工作，在间断Galerkin（DG）、加权本质无振荡（WENO）数值方法的研究及其应用方面取得了一些重要成果，已发表论文一百多篇。主持国家自然科学基金重点项目、联合基金重点支持项目和国家重点研发项目之课题各一项, 参与欧盟第六框架特别研究项目, 是项目组中唯一非欧盟的成员，多次应邀在国际会议上作大会报告。获2020年度教育部自然科学奖二等奖，2021年度福建省自然科学奖二等奖各一项。

摘要：

  In this presentation, we would give a brief review on a class of high-order weighted essentially non-oscillatory (WENO) schemes which are based on Hermite polynomials and termed HWENO (Hermite WENO) schemes, for solving nonlinear hyperbolic conservation law systems. The construction of HWENO schemes is based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge-Kutta methods. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. Comparing with the original WENO schemes of Liu et al. [J. Comput. Phys. 115 (1994) 200] and Jiang and Shu [J. Comput. Phys. 126 (1996) 202], one major advantage of HWENO schemes is its compactness in the reconstruction. For example, five points are needed in the stencil for a fifth-order WENO (WENO5) reconstruction, while only three points are needed for a fifth-order HWENO (HWENO5) reconstruction in one dimensional case. Numerical results are presented for both one and two dimensional cases to show the efficiency of the schemes.