报告题目：Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws
主讲人：李佳音 博士 （北京大学重庆大数据研究院）
李佳音博士，目前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，博士生导师为邱建贤教授，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。在国际顶尖杂志Journal of Computational Physics、Communications in Computational Physics发表过文章。
In this talk, 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 troubled-cells, 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 can also be any positive numbers as long as their sum equals one and the CFL number can still be 0.6 whether for the one or two dimensional case. Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.