主讲人简介:王晓明，本科及硕士毕业于复旦大学，博士毕业于美国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，由剑桥大学出版社出版专著1本，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。

内容摘要:We report on a few recent results related to thermal convection in afluid 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 Rayleighnumber crosses a threshold value is studied via a hybrid approach that combinesanalysis 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 ofthe most unstable mode from the lowest possible horizontal wave number tohigher wave numbers which could occur with variation of the height ratio aswell 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.

讲座主持:秦玉明教授