Convection in a coupled free-flow porous media flow system

PDE Seminar
Tuesday, January 21, 2020 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Prof. Xiaomin Wang – Southern University of Science and Technology –
Ronghua Pan

We show that the Principle of Exchange of Stability holds for convection in a layer of fluids overlaying a porous media with proper interface boundary conditions and suitable assumption on the parameters. The physically relevant small Darcy number regime as well as the dependence of the convection on various parameters will be discussed. A theory on the dependence of the depth ratio of the onset of deep convection will be put forth together with supporting numerical evidence. A decoupled uniquely solvable, unconditionally stable numerical scheme for solving the system will be presented as well.