New contributions to the solution of transport equations in porous media

In this article recent new developments in the method of decomposition as applied to the general solution of the three-dimensional deterministic/stochastic transport equation in heterogeneous porous media are presented with several applications to convection-dispersion models, spatial scale-dependent and time scale-dependent dispersion equations in heterogeneous porous media, simulation examples with coefficients of variability of up to 500%, and verification with exact solutions. The decomposition method offers fundamental advantages that could be used to build a more realistic theory of groundwater flow and contaminant transport than the current small perturbations theories.