Stochastic flow modelling in terms of interactive perturbation, Feynman diagrams and graph theory

The stochastic modeling of groundwater flow is considered. It is pointed out that in many circumstances analysis in terms of the ordinary perturbation series method may be incapable of representing fundamental characteristics of flow, and may lead to physically unreasonable solutions of the stochastic flow equation. To support this argument, the case of 1-D steady-state flow is examined using ordinary perturbation methods. Then, a more advanced interactive perturbation approach is introduced. This approach goes beyond standard perturbation approximation and can be used in situations where the interactions between flow terms is so significant that the ordinary low-order perturbation approximation will not work. The stochastic flow problem is then analyzed using concepts and techniques from stochastic turbulence and quantum field theory. These well-established techniques yield results similar to those of the interactive perturbation approach, a fact that proves the power of the latter