腾讯会议链接: //meeting.tencent.com/s/77O4cv7e8pdu 会议 ID：165 671 810
邀请人：⾼洪俊教授
内容摘要:
We discuss thermal convection in a fluid layer overlying a saturatedporous media based on the Navier-Stokes-Darcy-Boussinesq (NSDB) model withappropriate interface boundary conditions. The existence of global in time weaksolution for the NSDB system together with a weak-strong uniqueness result arepresented first. The stability of the pure conduction state at small Rayleigh number isintroduced 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 transitionbetween shallow and deep convection associated with the variation of the ratio of freeflow to porous media depth is accompanied by the change of the most unstable modefrom the lowest possible horizontal wave number to higher wave numbers which couldoccur with variation of the height ratio as well as the Darcy number and the ratio ofthermal diffusivity among others.Numerical methods that decouples the heat, the freeflow, the porous media flow while maintaining energy stability are presented as well.Wealso reconcile different interface boundary conditions at small Darcy number.
报告人简介: Dr. Wang received his BS and MS from Fudan University. He earned hisPh.D. from Indiana University Bloomington and received his postdoctoral training atCourant Institute. Dr. Wang's research focuses on modern applied mathematics,especially those related to fluid, geophysical fluid, and groundwater studies. Onecharacteristic of his research is the symbiosis of rigorous mathematics with genuineapplications. He was a tenured full professor and Chair of the Mathematics Departmentat The Florida State University before returning to his ancestral country. He is currently aChair Professor at Southern University of Science and Technology (SUSTech) and servingas the Head of the Mathematics Department at SUSTech and the Deputy Director of theNational Center for Applied Mathematics Shenzhen (NaCAMS).