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）

地点：致远楼108室

时间：2024年6月14日 星期五 下午5:00-6:00

摘要：In this presentation, we introduce a fifth-order moment-based Hermite weighted essen[1]tially 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 discretizations 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 pro[1]cedures 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 func[1]tion u and its non-zero multiple ζu. 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，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。

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