报告题目：On the data assimilation of initial distribution for 2-dimensional shallow-water equation model
报 告 人：刘继军（东南大学 教授）
会议时间：2023/11/27 上午09:30开始
会议地点：9-113
报告摘要：The data assimilation (DA) techniques are widely applied to estimate the full state of the system in marine meteorology, to overcome the practical restrictions that the measurement data can only be specified at finite discrete points in a small domain. We develop an efficient DA algorithm for recovering the initial status of the shallow-water equations (SWE) in a 2-dimensional rectangle domain from measurable sparse spatial data, involving both the complete Coriolis force and ocean bottom topography in the SWE model. After establishing the uniqueness of the solution to the nonlinear shallow-water equations with appropriate boundary conditions, we establish the conservation laws for suitably defined energy quantity for this traveling wave system, which generalizes the known conservation laws for the simplified SWE system ignoring the Coriolis force and topography, revealing the influence of nonconstant sea floor topography on wave propagation. Then for recovering the initial status by minimizing a cost functional using data assimilation, we derive the adjoint-problem for our iteration process and establish a discrete scheme for the governed equations in Arakawa C-grid for which the error for the energy conservation in discrete form is rigorously derived. The numerical implementations are also given to validate our proposed scheme by verifying the energy conservations and reconstruction effect of initial status for different configurations.
报告人简介：刘继军，东南大学二级教授，博士生导师，享受国务院政府特殊津贴专家。现任南京应用数学中心常务副主任，全国大学生数学建模竞赛组委会委员，江苏省计算数学学会副理事长。长期从事数学物理反问题、大规模科学计算和介质成像的数学理论和方法的研究。主持完成国家自然科学基金重大研究计划培育项目、面上项目、国际合作项目、天元基金、中国博士后科学基金、江苏省自然科学基金等项目。已在SIAM J. Appl. Math.等发表学术论文100余篇，在科学出版社出版学术专著2本。012-2017年任Inverse Problems in Sciences and Engineering编委，2018年起任J. Inverse and Ill-posed Problems编委。入选江苏省青蓝工程青年骨干教师，青蓝工程中青年学术带头人，江苏省333工程第三层次培养人选。获宝钢教育基金会全国优秀教师一等奖，作为主持人获江苏省教学成果一等奖、江苏省自然科学三等奖、教育部自然科学二等奖。
