报告题目：Thermal convection in superposed free flow and porous media: analysis and numerics

报 告 人：王晓明 教授 南方科技大学

邀请人：王裴昕

报告时间：2022年11月28日（周一）10：00-11：00（北京时间）

腾讯会议ID：268-677-962

会议密码：221128

报告人简介：王晓明教授本科和硕士毕业于复旦大学，1996年获得美国印第安那大学布鲁明顿分校博士学位。随后两年，在纽约大学著名的库朗研究所从事博士后研究（库朗讲师）；1998年加入爱荷华州立大学数学系，2001年晋升为副教授并获终身教职；2002年先后在库朗研究所和普林斯顿高等研究院担任研究员；2003年受邀加盟佛罗里达州立大学，任终身教授，2006晋升为正教授。在佛罗里达州立大学任职期间，曾担任应用和计算数学主任（2009-2012）和数学系系主任（2012-2017）。2017年受邀加盟母校复旦大学，任特聘教授；2018年加盟南科大，现任数学系系主任、讲席教授、深圳国家应用数学中心执行主任。

王晓明教授的研究重点是应用和计算数学，尤其是与气候变化和地下水研究有关的数学问题。他的工作的一个显著特点是严谨的数学和真实应用的有机结合。已在剑桥大学出版社出版专著一本，在CPAM等杂志发表学术论文100余篇。

报告摘要:

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.

We first discuss the relationship between various seemingly competing interfacial conditions at the physically important small Darcy number regime. 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. We propose a coarse-grained theory for the transition between shallow and deep convection and validate the coarse theory by comparing to direct numerical simulation and other works. Numerical methods that decouples the heat, the free flow, the porous media flow while maintaining energy stability are presented as well.

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