报告题目：A moment-based Hermite WENO scheme with unified stencils for hyperbolic conservation laws
报告人：邱建贤教授，厦门大学数学科学学院
报告时间：2025年6月16日（周一）下午14:00-15:30
报告地点：教2-327会议室
主办单位：南京邮电大学理学院
邀请人：朱洪强
报告内容：
In this presentation, we introduce a fifth-order moment-based Hermite weighted essentially non-oscillatory scheme with unified stencils (termed as HWENO-U) for hyperbolic conservation laws. The main idea of the HWENO-U scheme is to modify the first-order moment by a HWENO limiter only in the time discretization using the same information of spatial reconstructions, in which the limiter not only overcomes spurious oscillations well, but also ensures the stability of the fully-discrete scheme. For the HWENO reconstructions, a new scale-invariant nonlinear weight is designed by incorporating only the integral average values of the solution, which keeps all properties of the original one while is more robust for simulating challenging problems with sharp scale variations. Compared with previous HWENO schemes, the advantages of the HWENO-U scheme are: (1) a simpler implemented process involving only a single HWENO reconstruction applied throughout the entire procedures without any modifications for the governing equations; (2) increased efficiency by utilizing the same candidate stencils, reconstructed polynomials, and linear and nonlinear weights in both the HWENO limiter and spatial reconstructions; (3) reduced problem-specific dependencies and improved rationality, as the nonlinear weights are identical for the function $u$ and its non-zero multiple $\zeta u$. Besides, the proposed scheme retains the advantages of previous HWENO schemes, including compact reconstructed stencils and the utilization of artificial linear weights. Extensive benchmarks are carried out to validate the accuracy, efficiency, resolution, and robustness of the proposed scheme.
报告人简介：
邱建贤，厦门大学数学科学学院教授。主要研究方向包括计算流体力学、求解双曲守恒律等方程的高分辨数值方法等。他在间断Galerkin（DG）方法和加权本质无振荡（WENO）方法方面取得了丰硕的成果，共发表高水平学术论文160篇。他获得2020年度高等学校科学研究优秀成果奖（科学技术）--自然科学奖二等奖，2021年度福建省科学技术奖--自然科学奖二等奖。