Resolving vibro‐acoustics in poroelastic media via a multiscale virtual element method

Abstract

We introduce a novel heterogeneous multi-scale method for the frequency response analysis of waves propagating in porous domains with a complex micro-structure. In this, the domain is decomposed onto polygonal coarse elements each clustering its local micro-structure. The micro-structure is resolved using the virtual element method hence providing ample flexibility into capturing fine scale heterogeneities of arbitrary polygonal shapes. The upscaling is performed through a set of numerically evaluated multi-scale basis functions.Rather than evaluating the basis for a broad band set of frequencies, a reduced order modeling approach is opted for. In this, the basis is evaluated for a select subset of frequencies, that is used as a basis for the evaluation of the remaining set through a proper orthogonal decomposition procedure. The solution of the coupled governing equations is then performed at the coarse-scale at a reduced computational cost. 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.