报告题目: The Sharp Material Interface Limit in the Darcy-Boussinesq Model
报 告 人: 王晓明教授
报告时间: 2025年4月21日（周一）10:30-12:30
报告地点: 理工H楼306
报告摘要: Convection in porous media plays a fundamental role in geophysical fluid dynamics, geothermal energy, carbon sequestration, and many other climate-related processes. Layered porous structures often arise naturally or through design in various physical settings. In this talk, we investigate convection in such media using the Darcy–Boussinesq model. When material properties change abruptly between layers, the system becomes a nonlinear transmission problem, prompting the fundamental question of what interfacial (transmission) conditions are appropriate.
We address this by analyzing a sharp interface model as the limit of a more physically realistic formulation with diffuse material transitions, where properties vary smoothly across layers. Assuming constant porosity, we rigorously prove that as the thickness of the transition layers tends to zero, solutions of the diffuse model converge to those of the classical sharp interface model widely adopted in the fluid mechanics literature. The analysis uncovers the formation of velocity boundary layers and involves subtle estimates for elliptic and parabolic equations with (nearly) discontinuous coefficients.
This work provides a rigorous mathematical foundation for the sharp interface approximation, linking it to a more physically accurate diffuse-interface model. We also discuss implications for the long-time dynamics of the limiting system and outline numerical methods suited for such layered structures.
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数学科学学院
2025年4月18日
专家简介: 王晓明教授本科及硕士阶段就读于复旦大学数学系，后赴美在印第安纳大学伯明顿分校获得应用数学博士学位，并在纽约大学库朗数学科学研究所完成博士后研究。2024年起，王教授加入东方理工大学，担任数学学科创校讲席教授。在此之前，他曾在多所高校担任终身教职，包括密苏里科技大学首任 Havener 讲席系主任、南方科技大学讲席教授、复旦大学特聘教授、佛罗里达州立大学教授，以及爱荷华州立大学终身副教授。王教授同时也是国家特聘专家。
王晓明教授长期致力于现代应用数学前沿研究，主要方向包括流体动力学、地下水流动、地球物理流体力学、湍流与气候变化等。他善于融合偏微分方程、动力系统、随机分析、数值方法、科学计算及机器学习等多种数学工具，致力于在严谨数学理论与复杂物理系统之间架起桥梁，推动理论突破与交叉创新。他已在《Communications on Pure and Applied Mathematics》（CPAM）等国际一流期刊发表学术论文一百余篇，并由剑桥大学出版社出版学术专著一本。