Multiscale VEM for the Biot consolidation analysis of complex and highly heterogeneous domains

We introduce a novel heterogeneous multi-scale method for the consolidation analysis of two-dimensional porous domains with a complex micro-structure. A two-scale strategy is implemented wherein an arbitrary polygonal domain can be discretized into clusters of polygonal elements, each with its own set of fine scale discretization. The method harnesses the advantages of the Virtual Element Method into accurately capturing fine scale heterogeneities of arbitrary polygonal shapes. The upscaling is performed through a set of numerically evaluated multi-scale basis functions. The solution of the coupled governing equations is performed at the coarse-scale at a reduced computational cost. We discuss the computation of the multi-scale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples for poro-elastic materials with heterogeneities of various shapes