In this presentation, we introduce a robustfifth orderfinite difference Hermite weighted essentially non-oscillatory (HWENO) scheme for compressible Euler equations following the HWENO with limiter (HWENO-L) scheme (J. Comput. Phys., 472:111676, 2023). The HWENO-L scheme reduced storage and increased efficiency by using restricted derivatives only for time discretizations, however, it cannot control spurious oscillations well when facing strong shocks since the derivatives are directly used in spatial discretizations without any restrictions. To address such an issue, our proposed HWENO scheme performsflux reconstructions in thefinite difference framework without using the derivative value of a target cell, which can result in a simpler and more robust scheme. The resulting scheme is simpler while still achievingfifth order accuracy, so is more efficient. Besides, numerically wefind it is very robust for some extreme problems even without positivity-preserving limiters. The proposed scheme also inherits advantages of previous HWENO schemes, including arbitrary positive linear weights in theflux reconstructions, compact reconstructed stencils, and high resolution. Extensive numerical tests are performed to demonstrate thefifth order accuracy, efficiency, robustness, and high resolution of the proposed HWENO scheme.

报告人简介：

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。