A finite difference method for a coupled model of wave propagation in poroelastic materials.
A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.
Department of Earth, Atmospheric and Planetary Sciences, Earth Resources Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. yangz@mit.edu
Yang
Y
Zhang
Limin
L
Song
Max
M
Deffenbaugh
M Nafi
MN
Toksöz
D000162:Acoustics; D003198:Computer Simulation; D004548:Elasticity; D008962:Models, Theoretical; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D016062:Porosity; D015203:Reproducibility of Results; D013016:Sound; D013997:Time Factors