报告人：李佳音（北京大学重庆大数据研究院）

时间：2024年04月02日 15:00-

地点： 理科楼LA107

摘要：In this work, a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J. Comput. Phys., 446 (2021) 110653], in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the boundaries. However, in this paper, only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order moments. In addition, an extra modification procedure is used to modify those first order moments in the troubledcells, which leads to an improvement of stability and an enhancement of resolution near discontinuities. To obtain the same order of accuracy, the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the general WENO scheme. Moreover, the linear weights are not unique and are independent of the node position, and the CFL number can still be 0.6 whether for the one or two dimensional case, which has to be 0.2 in the two dimensional case for other HWENO schemes. Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.

简介：李佳音博士，现在北京大学重庆大数据研究院从事博士后研究工作，开发CAE国产替代软件北达飞易，合作导师胡俊教授。2014年本科就读于中国地质大学（武汉）数学与应用数学专业，2018年直博进入厦门大学数学科学学院计算数学专业，2023年获得理学博士学位，博士生导师邱建贤教授，联合培养博士生导师是国际知名数学家舒其望教授。曾参与国防基础科研核科学挑战专题—适用一般状态方程问题的三维多介质流体力学高精度高分辨率欧拉算法，与四川中锐信息技术有限公司合作进行多介质可压缩Navier-Stokes方程ALE方法求解器及两种组件库的开发，主持中国博士后科学基金面上资助项目多组分流模型的高阶多分辨率HWENO方法研究。并在国际知名杂志Journal of Computational Physics、Communications in Computational Physics发表数篇文章。

邀请人：王坤

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