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

Abstract

AbstractWe 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.