tau-SIMPLE algorithm for the closure problem in homogenization of Stokes flows

Abstract:

Estimation of the permeability tensor is crucial for many natural and industrial porous media applications. Homogenization provides a rigorous framework to calculate effective parameters from pore-scale images of a representative unit cell of the porous medium by solving a boundary value problem, also known as closure problem, subject to global constraints. However, the latter are hard to satisfy for arbitrarily complex geometries. We have developed a novel computational algorithm to calculate rigorously the permeability tensor. The approach, here referred to as tau-SIMPLE, is based on introducing an artificial time scale tau to satisfy the global constraint within the SIMPLE iteration. We show that the proposed algorithm has high accuracy for both two-dimensional and three-dimensional periodically arranged geometries.