中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
（第84讲）
(The Institute Lecture)
报告人： 王晓明 教授（南方科技大学）
题 目：Thermal convection in superposed free flow and porous media: analysis and numerics
时 间：2021.04.07 (星期三), 15:00-16:30(14:30-15:00为茶点时间, 地点: 数学院南楼N920室)
地 点：数学院南楼N204室
摘 要:
We discuss thermal convection in a fluid layer overlying a saturated porous media based on the Navier-Stokes-Darcy-Boussinesq (NSDB) model with appropriate interface boundary conditions.
The existence of global in time weak solution for the NSDB system together with a weak-strong uniqueness result are presented first.
The stability of the pure conduction state at small Rayleigh number is introduced next.
The loss of stability of the pure conduction state as the Rayleigh number crosses a threshold value is studied via a hybrid approach that combines analysis with numerical computation.
In particular, we discover that the transition between shallow and deep convection associated with the variation of the ratio of free-flow to porous media depth is accompanied by the change of the most unstable mode from the lowest possible horizontal wave number to higher wave numbers which could occur with variation of the height ratio as well as the Darcy number and the ratio of thermal diffusivity among others.
Numerical methods that decouples the heat, the free flow, the porous media flow while maintaining energy stability are presented as well.
We also reconcile different interface boundary conditions at small Darcy number.
王晓明教授简介:
王晓明本科及硕士毕业于复旦大学，博士毕业于印第安纳大学布卢明顿分校，主要研究方向为应用偏微分方程及其数值方法，在CPAM、JFM、SINUM等杂志发表论文90多篇，系中组部认定的国家级人才；曾任职纽约库朗研究所、普林斯顿高等研究院、爱荷华州立大学、复旦大学。回国前为美国佛罗里达州立大学长聘正教授和数学系系主任，现任南方科技大学数学系系主任、讲席教授，深圳国家应数中心执行主任。
数学所讲座(The Institute Lecture)：
旨在讲解现代数学的重要内容及其思想、方法和影响，扩展我们科研人员和研究生的视野、提高数学修养和加强相互交流、增强学术气氛。时间定在每月（寒暑假另外安排）的第一个星期三。
