Staggered finite volume algorithms for dynamic analysis of saturated soil with low permeability and incompressible pore fluid by using OpenFOAM

Abstract

Biot dynamic theory forms the basis of dynamic analysis for soil-pore fluid coupling, whose formulations can be simplified by u-p approximation for low frequency phenomena without loss of accuracy. In the past decades, fully-coupled approach and segregated method were two common strategies for Finite Volume (FV) solutions to Biot dynamic theory. However, both methods encounter problems that limit their applicability when soil permeability and pore fluid compressibility reduce to a relatively low level. Under this circumstance, fully-coupled approach requires mixed formulation to satisfy Babuška-Brezzi condition, which complicates numerical implementation. On the other hand, segregated method suffers from divergence and instability, and shows poor performance in computation efficiency. In this article, two staggered FV algorithms incorporating operator splitting technique are devoted to overcoming the aforementioned shortcomings, and they are implemented on the open-source, broadly used and versatile platform for FV calculation, OpenFOAM. Through comparing the computed results of the two algorithms with solutions in the literature, both of the proposed algorithms are shown to reasonably reflect the dynamic responses of porous media. By conducting stability analyses based on the numerical cases, the two algorithms are shown to enlarge the stability region and enable larger time steps for computation.