Modeling and simulating finite-amplitude propagation through time-varying inhomogeneous absorbing media

A model equation is derived for three-dimensional wave propagation through an inhomogeneous, time-varying medium. The model equation accounts for arbitrary inhomogeneities, finite-amplitude distortion, and absorption. The effect of time dependence of the background medium parameters is included in the equation. An ordering scheme based on the characteristic time of the evolution of each parameter allows one to evaluate their relative importance. A two-dimensional version of the wave equation is solved in the time-domain using finite-difference methods. Explicit, implicit, and operator splitting techniques were used in the solution to overcome numerical instabilities. Results from the code are compared to known solutions for some simple geometries in homogeneous and step indexed media. Various modeling and numerical schemes for treating the absorption on the computational domain interior and at the boundaries of the domain will be presented. [Work supported by ONR and DARPA.]