Modelling sound propagation through layered porous media
 

Hello---

I would like to set up a CFD problem that models the propagation of an acoustic pulse through a layered porous (Biot-type) medium. Here is the physical setup of the system that I would like to model.

An acoustic source is situated in the air above the surface of the layered porous medium. The pore space of each layer in the medium contains an unsaturated mixture of air and water and each layer has different physical properties. The source radiates an arbitrary sound pulse toward the layered porous medium. This implies that the source function is not analytic, and can be updated at every time step.

The sound wave incident at the air-medium interface couples into the porous medium. Reflections occur at the air-medium interface and at each of the interfaces in the porous medium.

The porous medium (fluid and frame) should have a temperature and thermal properties. At this time, I would like to model the effects of temperature on the sound wave, and not the transport of heat and energy.

The boundary conditions should approximate free-field conditions. I believe that this would entail using some form of Perfectly Matched Layer (PML) to attenuate reflections.

I would like to determine the RMS pressure of reflections from the layered porous medium at arbitrary points in the air above the surface of the porous medium.

How should I begin? I suspect that I should do one of the following:

(1) model the porous medium using FEM; or
(2) use Green's function solutions to generate a synthetic seismogram
(but can this be done for an arbitrary source function?)

Essentially what I am looking for is:

(1) A good reference on the equations used to set up this model, showing how to couple the unsaturated porous medium with the thermal conditions.

(2) If available, a code or solver which may help with the setup and modeling of this physical system. Could this model be set up using COMSOL or OpenFOAM?