学术报告报告题目：On the OP-Mapped WENO Schemes
报 告人：钟巍 博士
报告时间：2022年9月23日（星期五）下午3:00—5:00
报告地点：四号楼4318会议室
邀 请人：姚文琦 副教授何志坚教授
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数学学院
2022年9月21日
报告摘要：In this talk, we report the WENO schemes with order-preserving mappings, dubbed OP-Mapped WENO. Since WENO schemes can achieve high order accuracy in smooth regions while preventing spurious oscillations near discontinuities, they have become one of the most popular methods for approximating solutions to hyperbolic conservation laws. However, in long-run simulations, it seems to be very different and extremely challenging for WENO schemes to obtain considerably high resolutions and meanwhile avoid spurious oscillations. A number of studies have indicated that most of the existing WENO schemes suffer from either losing high resolutions or generating spurious oscillations on solving hyperbolic problems with discontinuities at large output times. During the last decade, this issue has attracted considerable scholarly interest but the way of completely addressing it has remained unclear up to now. We conduct a systematical investigation on various existing mapped WENO schemes and reveal the essential reason of the issue mentioned above. It is actually caused by that the mapping functions of these schemes can not preserve the order of the nonlinear weights of the stencils. In other words, the nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils unfavorably. According to this knowledge, we develop the novel concept of order-preserving (OP) mapping, and this provides a new direction for both devising new WENO schemes and improving the existing ones. Extensive numerical experiments demonstrate that the WENO schemes which adopt OP mappings exhibit remarkable advantages for long-run simulations, such as attaining high resolutions and in the meantime avoiding spurious oscillations near discontinuities, as well as obtaining high resolutions on solving problems with high-order critical points. Furthermore, even in short-time simulations, they also gain several considerable enhancements, such as improving resolutions in the regions with high-frequency smooth waves, removing or significantly reducing post-shock numerical oscillations on solving the two-dimensional problems with shock waves, as well as greatly limiting numerical oscillations in the framework of component-wise reconstruction. (This is a joint work with Prof. Ruo Li.)
报告人简介：钟巍，副研究员，西北核技术研究院总体所力学室副主任、党支部副书记，单位力学学科建设负责人。本科毕业于清华大学航天航空工程学院工程力学与航天航空工程专业，获工学学士学位，博士毕业于北京大学数学科学学院计算数学专业，获理学博士学位，导师为李若教授。主要从事计算流体力学、高精度数值算法、爆炸冲击波传播与毁伤效应、化学反应动力学等相关研究，在IJIE、CiCP、AMC、AAMM、NMTMA、MCA及《计算数学》、《数值计算与计算机应用》、《计算物理》、《力学学报》、《兵工学报》、《爆炸与冲击》、《岩土工程学报》等国内外知名期刊发表学术论文近50篇，其中SCI、EI检索30余篇。获部委级优秀硕士学位论文奖，获第二十届中国空气动力学物理气体动力学学术交流会优秀论文奖，入选Axioms、Computers、IJGI期刊创刊十周年精选优秀论文。担任中国空气动力学学会物理气体动力学专委会委员和AMC、《含能材料》等期刊审稿人。作为项目负责人主持完成多个重点项目，项目总经费超过1000万。享受部委级优秀专业技术人才岗位津贴，入选部委级高层次科技创新人才工程。