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Flow and transport when scales are not separated: Numerical analysis and simulations of micro- and macro-models Public Deposited

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  • In this paper, we consider an upscaled model describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium. Unlike traditional homogenization or volume averaging techniques, we do not assume a good separation of scales. The new model includes as special cases both the classical homogenized model and the double porosity model, but it is characterized by the presence of additional memory terms which describe the effects of local advective transport as well as diffusion. We study the mathematical properties of the memory (convolution) kernels presented in the model and perform rigorous stability analysis of the numerical method to discretize the upscaled model. Some numerical results will be presented to validate the upscaled model and to show the quantitative significance of each memory term in different regimes of flow and transport.
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  • Peszynska, M., Showalter, R. E., & Yi, S. Y. (2015). Flow and transport when scales are not separated: Numerical analysis and simulations of micro-and macro-models. International Journal of Numerical Analysis and Modeling, 12(3), 476-515.
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  • 12
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  • This work was supported by the grant DOE-98089 “Modeling, analysis, and simulation of preferential flow in porous media”. Research of Peszy´nska was also partially supported by the NSF-DMS-0511190 “Modeling adaptivity for porous media” and NSF-DMS 1115827 “Hybrid modeling in porous media.”
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