Abstract
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.
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