Flow, transport and diffusion in random geometries II: applications

Abstract

Multilevel Monte Carlo (MLMC) is an efficient and flexible solution for the propagation of uncertainties in complex models, where an explicit parametrization of the input randomness is not available or too expensive. We present several applications of our MLMC algorithm for flow, transport and diffusion in random heterogeneous materials. The absolute permeability and effective diffusivity (or formation factor) of micro-scale porous media samples are computed and the uncertainty related to the sampling procedures is studied. The algorithm is then extended to the transport problems and multiphase flows for the estimation of dispersion and relative permeability curves. The impact of water drops on random stuctured surfaces, with microfluidics applications to self-cleaning materials, is also studied and simulated. Finally the estimation of new drag correlation laws for poly-dispersed dilute and dense suspensions is presented.