Resolving vibro-acoustics in double porosity materials via a coupled multiscale finite element method

Acoustic materials with non-standard material and geometrical layouts are deployed in buildings to improve sound absorption at targeted frequency bandwidths. Classical numerical models such as the Finite Element Method (FEM) can prove prohibitively expensive as very fine mesh discretizations are required to resolve high frequency waves and complex meso-scale morphologies. Upscaling methodologies like the Coupling Multiscale Finite Element Method (CMsFEM) can be used to achieve accelerated modelling strategies without significantly sacrificing accuracy. Here, complex interfaces and heterogeneous morphologies are resolved at the fine scale. These are mapped onto the coarse scale through a set of numerically evaluated basis functions. The governing equations are finally solved at the coarse-scale at a reduced computational cost. We originally apply the CMsFEM to the Biot equations for wave propagation in poroelastic media and employ it to treat porous materials with mesoscale perforations, i.e., double porosity materials. The efficiency and accuracy of the method are discussed with respect to numerical applications, using an in-house MATLAB code.