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

A novel dispersive model for wave propagation in heterogeneous media is dev eloped. The method is based on a higher-order mathematical homogenization t heory with multiple spatial and temporal scales. By this approach a fast sp atial scale and a series of slow temporal scales are introduced to account for rapid spatial fluctuations of material properties as well as for the lo ng-term behavior of the homogenized solution. The problem of secularity ari sing from the classical multiple-spatial-scale homogenization theory for wa ve propagation problems is resolved, giving rise to a uniformly valid dispe rsive model. The proposed dispersive model is solved analytically and its s olution is found to be in good agreement with the numerical solution of the source problem in a heterogeneous medium.