Numerically Solving the Biot Equations for Sound Absorbing Materials Using a Wave Expansion Method

Poro-elastic materials are often used in noise control applications where they are connected to a fluid medium in order dissipate acoustic waves through viscous, thermal and structural effects. The prediction of sound propagation in such materials is therefore of practical interest for many engineering applications. This propagation may be described by the Biot equations. In this paper, a numerical approach known as a wave expansion method is developed to solve the Biot equations. A wave expansion method uses fundamental solutions of the wave operator and so accurate solutions to linearized propagation equations may be obtained with only two-to-three points per wavelength. The method is also robust to meshing and could be implemented in a meshless manner. These characteristics make it well suited to examining practical sound absorption applications. The method is applied to a benchmark problem and the results are compared to the analytical solution. The results are found to be very promising.