报告题目：High-order finite volume Hermite WENO schemes for hyperbolic conservation laws on triangular meshes
报 告 人：赵状 副教授
所在单位：厦门大学
报告时间：2024年9月6日 星期五 下午 16:00-17:00
报告地点：数学楼第二报告厅
校内联系人：陶詹晶 zjtao@jlu.edu.cn
报告摘要：
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.
报告人简介：
赵状，厦门大学数学科学学院副教授，入选厦门大学南强青拔B类人才计划。2021年博士毕业于厦门大学，曾于上海交通大学从事博士后研究工作。主要关注欧拉方程、磁流体力学方程和多介质流问题的 WENO 和 HWENO方法研究。在Journal of Computational Physics, Science China Mathematics 和 Computer Methods in Applied Mechanics and Engineering 等期刊发表论文十余篇。曾获中国博士后基金面上项目资助和福建省自然科学优秀学术论文一等奖。
