THE PHONONIC LATTICE SOLID WITH FLUIDS FOR MODELING NONLINEAR SOLID-FLUID INTERACTIONS

The phononic lattice solid has been developed recently as a possible a pproach for modelling compressional waves in complex solids at the mic roscopic scale. Rather than directly modelling the wave equation, the microdynamics of quasi-particles is simulated on a discrete lattice. I t is comparable with the lattice gas approach to model idealized gas p articles but differs fundamentally in that lattice solid particles car ry pressure rather than mass and propagate through a heterogeneous med ium. Their speed may be space and direction dependent while the speed of lattice gas particles is constant. Furthermore, they may be scatter ed by medium heterogeneities. Lattice sites in the phononic lattice so lid approach are considered to be fixed in space for all time. Lattice site movements (i.e. deformations) induced by the passage of a macros copic wave are particularly important for a fluid-filled porous medium considering that non-linear solid-fluid interactions are thought to p lay a role in attenuation mechanisms. We take lattice site movements i nto account in the phononic lattice solid and name the approach 'the p hononic lattice solid with fluids (PLSF)' because it could lead to an improved understanding of the effect of solid-fluid interactions in wa ve propagation problems. The macroscopic limit of the Boltzmann equati on for the PLSF yields the acoustic wave equation for heterogeneous me dia modified by shear and bulk viscosity terms as well as the second-o rder term in macroscopic velocity (for the PLS) and additional non-lin ear terms due to the lattice site movements. It is hoped that PLSF num erical simulation studies of waves through digitized rock matrices may lead to an improved understanding of attenuation mechanisms of waves in porous rocks.