Uniformly valid multiple spatial-temporal scale modeling for wave propagation in heterogeneous media

A novel dispersive model for wave propagation in heterogeneous media is developed. The method is based on a higher-order mathematical homogenization theory with multiple spatial and temporal scales. By this approach a fast spatial scale and a series of slow temporal scales are introduced to account for rapid spatial fluctuations of material properties as well as for the long-term behavior of the homogenized solution. The problem of secularity arising from the classical multiple-spatial-scale homogenization theory for wave propagation problems is resolved, giving rise to a uniformly valid dispersive model. The proposed dispersive model is solved analytically and its solution is found to be in good agreement with the numerical solution of the source problem in a heterogeneous medium.