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The paper is devoted to the homogenization of Richards' type equations in a deterministic multiscale porous medium filled with soft inclusions. The medium consists of a deterministic ensemble of coarse aggregates embedded within a matrix containing a deterministic ensemble of fine aggregates, leading to a network in which the inclusions (of different sizes) are widely distributed. Under various settings involving the structure of the medium and the coefficients of the equation, we obtain homogenized limits of the underlying micro-model. We also provide a suitable approximation scheme for the homogenized coefficients, thereby providing a numerical method for computing these coefficients. To achieve our goal, apply tools of the multiscale sigma-convergence method. |
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