Aitken-Schwarz DDM to solve Darcy flow in heterogeneous underground mediums

The objective of this work is to show the potentiality of the Aitken-Schwarz domain decomposition method to simulate the transport of fluids solutions in heterogeneous underground mediums. To study the phenomenology of the hydraulic properties, we use a stochastic model, where the data are random variables according to a prescribed distribution. The techniques of homogenization to model the studied heterogeneous mediums do not apply, because characteristic scales do not exist. All the computing scales need to be taken in account and lead to develop extensible and effective numerical methods to analyze the effects of scalings. The physical modelling of the heterogeneous mediums leads to several types of difficulties even for the linear Darcy equation: { ∇.(k(x)∇h(x)) = f(x), x ∈ Ω ⊂ R Bh(x) = g(x), x ∈ ∂Ω (1)