The Correspondence between Voigt and Reuss Bounds and the Decoupling Constraint in a Two-Grid Staggered Algorithm for Consolidation in Heterogeneous Porous Media

Abstract

We establish a link between the decoupling constraint in a two-grid staggered solution algorithm for consolidation in heterogeneous porous media and the concepts of Voigt and Reuss bounds commonly encountered in the theory of computational homogenization of multiphase composites. Our analysis involves deriving bounds on a tuning parameter in the decoupling constraint for determining the speed and accuracy of the algorithm. An upper bound is obtained from theoretical convergence of the algorithm which leads to the fastest convergence. A lower bound is established by employing the concepts of Voigt and Reuss bounds. From these bounds, we conclude that there is a value for the tuning parameter between the bounds that gives the most accurate solution.