Numerical Calculation of Effective Density and Compressibility Tensors in Periodic Porous Media: A Multi-Scale Asymptotic Method

C. Lee[1], M. Leamy[1], and J. Nadler[2]

[1]School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA
[2]Georgia Tech Research Institute (GTRI), Georgia Institute of Technology
Published in 2008

A major issue in predicting and controlling (via design) absorption properties of rigid porous media is the determination of the frequency-dependent effective density and compressibility tensors. Unlike previous research efforts which employ in-house and, oftentimes, multiple numerical procedures for determining these two essential tensors, we formulate their solution in terms of a set of micro-scale governing equations (and associated boundary conditions) resulting from a multi-scale asymptotic analysis.

Incorporating the equations directly into COMSOL Multiphysics allows for arbitrary 3D model generation, unit cell meshing, and ultimate analysis using a single software package. We demonstrate the validity of this approach by comparing our numerical results with those published in the literature.