報告題目：High-order finite volume Hermite WENO schemes for hyperbolic conservation laws on triangular meshes
報 告 人：趙狀 副教授
所在單位：廈門大學
報告時間：2024年9月6日 星期五 下午 16:00-17:00
報告地點：數學樓第二報告廳
校内聯系人：陶詹晶 zjtao@jlu.edu.cn
報告摘要：
In this talk, we will introduce the high-order Hermite weighted essentially non-oscillatory (HWENO) schemes for two-dimensional hyperbolic conservation laws on triangular meshes. These schemes integrate both zeroth- and first-order moments into spatial discretizations, yielding more compact stencils than same-order WENO schemes. Specifically, the third- and fifth-order HWENO schemes require only one and two layers of stencils, respectively, as opposed to the two layers needed by a third-order WENO scheme. Meanwhile, the HWENO schemes demonstrate reduced numerical errors in smooth areas and improved resolution near discontinuities. Although the HWENO schemes include two auxiliary equations, they retain a unified nonlinear reconstruction process similar to that of WENO schemes. This design choice leads to a modest increase in computational expense and algorithm complexity. Crucially, an efficient definition of smoothness indicators is introduced, based on a midpoint numerical integration of the original indicator. This streamlined definition enhances computational efficiencies on unstructured meshes and results in only minor variations in smoothness measurement between the two definitions, regardless of whether the problem is smooth or discontinuous. The HWENO schemes are distinguished by their strong practicality on triangular meshes, with efficient computation of smoothness indicators, consistent use of a single set of compact stencils, and application of artificial linear weights. Extensive numerical experiments are conducted to verify the high-order accuracy, efficiency, resolution, robustness, scale-invariance, and the effectiveness of the smoothness indicator for the proposed HWENO schemes.
報告人簡介：
趙狀，廈門大學數學科學學院副教授，入選廈門大學南強青拔B類人才計劃。2021年博士畢業于廈門大學，曾于上海交通大學從事博士後研究工作。主要關注歐拉方程、磁流體力學方程和多介質流問題的 WENO 和 HWENO方法研究。在Journal of Computational Physics, Science China Mathematics 和 Computer Methods in Applied Mechanics and Engineering 等期刊發表論文十餘篇。曾獲中國博士後基金面上項目資助和福建省自然科學優秀學術論文一等獎。
