Computation of dynamic behavior of sound absorbing porous materials using efficient Fourier transform approach

In this paper, we propose an efficient FFT (Fast Fourier Transform) based numerical method to determine the acoustical properties of sound absorbing porous materials, including dynamic viscous and thermal permeability, from the pixelized/voxelized microstructure. At the local scale, the governing equations of the two problems are periodic and dynamic generalizations of Stokes and Laplace equations with inertial body terms depending on the excitation frequency $\omega$. To solve the problems in regular grids, the discrete frequency dependent Green’s functions of the two problems in Fourier space are obtained using finite difference approximation and used to construct boundary equations for the distribution of force and source terms. The equations can then be solved by iterative solvers for the two cases $\omega =0$ and $\omega \ne 0$, respectively. Numerical tests for different pixelized and voxelized porous microstructure confirm the good performance and accuracy of the method.