On the upscaling of the diffusion equation in a heterogeneous medium by the two different methods
Alexander A. Shapiro
Abstract:Upscaling the flow equations appears in many studies related to diffusion, heat conductivity, and flows in porous media. Variable coefficients of the original fine-scale process description are substituted by averaged constant values. The different upscaling procedures have been suggested in the literature. The question arises, whether they result in the same or different upscaled models; moreover, whether the solutions of the coarse-scale equations provide a reasonably accurate description of the fine scale. … Show more
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