Radiative transfer theory for high-frequency power flows in fluid-saturated, poro-visco-elastic media
Éric Savin · The Journal of the Acoustical Society of America · 2005
Some recent mathematical results are used to study the propagation features of the high-frequency vibrational energy density in three-dimensional fluid-saturated, isotropic poro-visco-elastic media. The theory of high-frequency asymptotics of the solutions of hyperbolic partial differential equations shows that their energy satisfies Liouville-type transport or radiative transfer equations for randomly heterogeneous materials. For long propagation times these equations can be approached by diffusion equations. The corresponding diffusion parameters—mean-free paths and diffusion constants—associated with Biot’s linear model for such media, are derived. The analysis accounts for the thermal and viscous memory effects of the fluid phase, and the viscous memory effect of the solid phase through time convolution operators. In this respect it also extends the existing mathematical results.