報告題目： A robust fifth order finite difference Hermite WENO scheme for compressible Euler equations
報 告 人：邱建賢 教授 廈門大學數學科學學院
報告時間：2023年5月19日 14:00-15:00
報告地點：伟德线上平台三樓研讨室6
校内聯系人：陶詹晶 zjtao@jlu.edu.cn
報告摘要：In this presentation, we introduce a robust fifth order finite 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 performs flux reconstructions in the finite 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 achieving fifth order accuracy, so is more efficient. Besides, numerically we find 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 the flux reconstructions, compact reconstructed stencils, and high resolution. Extensive numerical tests are performed to demonstrate the fifth order accuracy, efficiency, robustness, and high resolution of the proposed HWENO scheme.
報告人簡介：邱建賢，廈門大學數學科學學院教授，國際著名刊物 “J. Comp. Phys.” (計算物理) 編委。從事計算流體力學及微分方程數值解法的研究工作，在間斷 Galerkin（DG）、加權本質無振蕩（WENO）數值方法的研究及其應用方面取得了一些重要成果，已發表論文一百多篇。主持國家自然科學基金重點項目、聯合基金重點支持項目和國家重點研發項目之課題各一項, 參與歐盟第六框架特别研究項目, 是項目組中唯一非歐盟的成員，多次應邀在國際會議上作大會報告。獲2020年度教育部自然科學獎二等獎，2021年度福建省自然科學獎二等獎各一項。
