Influence of surface topography on Rayleigh-Darcy Convection in Porous Domain

A sharp interface-immersed boundary method (IBM) is employed to simulate the influence of rough surfaces on Rayleigh-Darcy convection in homogeneous porous media. The motivation for this investigation stems from the fact that the geophysical domains in which such convection occurs have uneven topography. The numerical framework combines a second-order central finite-difference scheme, a third-order Runge–Kutta integration method for advection, and an implicit alternating-direction (ADI) method for viscous and diffusive terms. The porous domain, saturated with fluid and bounded by hot and cold surfaces, incorporates topology. We quantify the heat transfer phenomenon and the boundary layer characteristics as a function of the shape, size, and number of topological features and provide a comparison with the classical flat-surface Rayleigh-Darcy convection.